diff --git a/src/Microsoft.ML.Core/Utilities/MathUtils.cs b/src/Microsoft.ML.Core/Utilities/MathUtils.cs
index e2848ea25d..8106ff5a2c 100644
--- a/src/Microsoft.ML.Core/Utilities/MathUtils.cs
+++ b/src/Microsoft.ML.Core/Utilities/MathUtils.cs
@@ -871,5 +871,16 @@ public static double Cos(double a)
             var res = Math.Cos(a);
             return Math.Abs(res) > 1 ? double.NaN : res;
         }
+
+        /// <summary>
+        /// Returns the smallest integral value that is greater than or equal to the result of the division.
+        /// </summary>
+        /// <param name="numerator">Number to be divided.</param>
+        /// <param name="denomenator">Number with which to divide the numerator.</param>
+        /// <returns></returns>
+        public static long DivisionCeiling(long numerator, long denomenator)
+        {
+            return (checked(numerator + denomenator) - 1) / denomenator;
+        }
     }
 }
diff --git a/src/Microsoft.ML.Parquet/ParquetLoader.cs b/src/Microsoft.ML.Parquet/ParquetLoader.cs
index f0ecde34dc..21271f6e5c 100644
--- a/src/Microsoft.ML.Parquet/ParquetLoader.cs
+++ b/src/Microsoft.ML.Parquet/ParquetLoader.cs
@@ -94,7 +94,7 @@ public sealed class Arguments
         private readonly int _columnChunkReadSize;
         private readonly Column[] _columnsLoaded;
         private readonly DataSet _schemaDataSet;
-        private const int _defaultColumnChunkReadSize = 100; // Should ideally be close to Rowgroup size
+        private const int _defaultColumnChunkReadSize = 1000000;
 
         private bool _disposed;
 
@@ -368,8 +368,8 @@ private sealed class Cursor : RootCursorBase, IRowCursor
             private readonly Delegate[] _getters;
             private readonly ReaderOptions _readerOptions;
             private int _curDataSetRow;
-            private IEnumerator _dataSetEnumerator;
-            private IEnumerator _blockEnumerator;
+            private IEnumerator<int> _dataSetEnumerator;
+            private IEnumerator<int> _blockEnumerator;
             private IList[] _columnValues;
             private IRandom _rand;
 
@@ -390,11 +390,18 @@ public Cursor(ParquetLoader parent, Func<int, bool> predicate, IRandom rand)
                     Columns = _loader._columnsLoaded.Select(i => i.Name).ToArray()
                 };
 
-                int numBlocks = (int)Math.Ceiling(((decimal)parent.GetRowCount() / _readerOptions.Count));
-                int[] blockOrder = _rand == null ? Utils.GetIdentityPermutation(numBlocks) : Utils.GetRandomPermutation(rand, numBlocks);
+                // The number of blocks is calculated based on the specified rows in a block (defaults to 1M).
+                // Since we want to shuffle the blocks in addition to shuffling the rows in each block, checks
+                // are put in place to ensure we can produce a shuffle order for the blocks.
+                var numBlocks = MathUtils.DivisionCeiling((long)parent.GetRowCount(), _readerOptions.Count);
+                if (numBlocks > int.MaxValue)
+                {
+                    throw _loader._host.ExceptParam(nameof(Arguments.ColumnChunkReadSize), "Error due to too many blocks. Try increasing block size.");
+                }
+                var blockOrder = CreateOrderSequence((int)numBlocks);
                 _blockEnumerator = blockOrder.GetEnumerator();
 
-                _dataSetEnumerator = new int[0].GetEnumerator(); // Initialize an empty enumerator to get started
+                _dataSetEnumerator = Enumerable.Empty<int>().GetEnumerator();
                 _columnValues = new IList[_actives.Length];
                 _getters = new Delegate[_actives.Length];
                 for (int i = 0; i < _actives.Length; ++i)
@@ -472,12 +479,12 @@ protected override bool MoveNextCore()
             {
                 if (_dataSetEnumerator.MoveNext())
                 {
-                    _curDataSetRow = (int)_dataSetEnumerator.Current;
+                    _curDataSetRow = _dataSetEnumerator.Current;
                     return true;
                 }
                 else if (_blockEnumerator.MoveNext())
                 {
-                    _readerOptions.Offset = (int)_blockEnumerator.Current * _readerOptions.Count;
+                    _readerOptions.Offset = (long)_blockEnumerator.Current * _readerOptions.Count;
 
                     // When current dataset runs out, read the next portion of the parquet file.
                     DataSet ds;
@@ -486,9 +493,9 @@ protected override bool MoveNextCore()
                         ds = ParquetReader.Read(_loader._parquetStream, _loader._parquetOptions, _readerOptions);
                     }
 
-                    int[] dataSetOrder = _rand == null ? Utils.GetIdentityPermutation(ds.RowCount) : Utils.GetRandomPermutation(_rand, ds.RowCount);
+                    var dataSetOrder = CreateOrderSequence(ds.RowCount);
                     _dataSetEnumerator = dataSetOrder.GetEnumerator();
-                    _curDataSetRow = dataSetOrder[0];
+                    _curDataSetRow = dataSetOrder.ElementAt(0);
 
                     // Cache list for each active column
                     for (int i = 0; i < _actives.Length; i++)
@@ -533,6 +540,26 @@ public bool IsColumnActive(int col)
                 Ch.CheckParam(0 <= col && col < _colToActivesIndex.Length, nameof(col));
                 return _colToActivesIndex[col] >= 0;
             }
+
+            /// <summary>
+            /// Creates a in-order or shuffled sequence, based on whether _rand is specified.
+            /// If unable to create a shuffle sequence, will default to sequential.
+            /// </summary>
+            /// <param name="size">Number of elements in the sequence.</param>
+            /// <returns></returns>
+            private IEnumerable<int> CreateOrderSequence(int size)
+            {
+                IEnumerable<int> order;
+                try
+                {
+                    order = _rand == null ? Enumerable.Range(0, size) : Utils.GetRandomPermutation(_rand, size);
+                }
+                catch (OutOfMemoryException)
+                {
+                    order = Enumerable.Range(0, size);
+                }
+                return order;
+            }
         }
 
         #region Dispose
@@ -671,4 +698,4 @@ private string ConvertListToString(IList list)
             }
         }
     }
-}
+}
\ No newline at end of file