diff --git a/stdlib/SparseArrays/src/sparsematrix.jl b/stdlib/SparseArrays/src/sparsematrix.jl
index a6e38fa356f02..ce2084d346284 100644
--- a/stdlib/SparseArrays/src/sparsematrix.jl
+++ b/stdlib/SparseArrays/src/sparsematrix.jl
@@ -800,7 +800,7 @@ function sparse!(I::AbstractVector{Ti}, J::AbstractVector{Ti},
         overwritten = csccolptr[j]
         csccolptr[j] = countsum
         countsum += overwritten
-        countsum <= typemax(Ti) || throw(ArgumentError("more than typemax(Ti)-1 == $(typemax(Ti)-1) entries"))
+        Base.hastypemax(Ti) && (countsum <= typemax(Ti) || throw(ArgumentError("more than typemax(Ti)-1 == $(typemax(Ti)-1) entries")))
     end
 
     # Now knowing the CSC form's entry count, resize cscrowval and cscnzval if necessary
diff --git a/stdlib/SparseArrays/test/sparse.jl b/stdlib/SparseArrays/test/sparse.jl
index 4ae8634a07316..d27746fe23759 100644
--- a/stdlib/SparseArrays/test/sparse.jl
+++ b/stdlib/SparseArrays/test/sparse.jl
@@ -55,6 +55,8 @@ end
     @test_throws ArgumentError sparse([1,2,4], [1,2,3], [1,2,3], 3, 3)
     @test_throws ArgumentError sparse([1,2,3], [1,2,4], [1,2,3], 3, 3)
     @test isequal(sparse(Int[], Int[], Int[], 0, 0), SparseMatrixCSC(0, 0, Int[1], Int[], Int[]))
+    @test isequal(sparse(big.([1,1,1,2,2,3,4,5]),big.([1,2,3,2,3,3,4,5]),big.([1,2,4,3,5,6,7,8]), 6, 6),
+        SparseMatrixCSC(6, 6, big.([1,2,4,7,8,9,9]), big.([1,1,2,1,2,3,4,5]), big.([1,2,3,4,5,6,7,8])))
     @test sparse(Any[1,2,3], Any[1,2,3], Any[1,1,1]) == sparse([1,2,3], [1,2,3], [1,1,1])
     @test sparse(Any[1,2,3], Any[1,2,3], Any[1,1,1], 5, 4) == sparse([1,2,3], [1,2,3], [1,1,1], 5, 4)
 end