diff --git a/lib/cusparse/conversions.jl b/lib/cusparse/conversions.jl
index 69dbaf3f9b..16528465f7 100644
--- a/lib/cusparse/conversions.jl
+++ b/lib/cusparse/conversions.jl
@@ -328,7 +328,7 @@ for elty in (:Float32, :Float64, :ComplexF32, :ComplexF64)
     @eval begin
         function CuSparseMatrixCSC{$elty}(csr::CuSparseMatrixCSR{$elty}; index::SparseChar='O', action::cusparseAction_t=CUSPARSE_ACTION_NUMERIC, algo::cusparseCsr2CscAlg_t=CUSPARSE_CSR2CSC_ALG1)
             m,n = size(csr)
-            colPtr = CUDA.zeros(Cint, n+1)
+            colPtr = CUDA.ones(Cint, n+1)
             rowVal = CUDA.zeros(Cint, nnz(csr))
             nzVal = CUDA.zeros($elty, nnz(csr))
             function bufferSize()
@@ -348,7 +348,7 @@ for elty in (:Float32, :Float64, :ComplexF32, :ComplexF64)
 
         function CuSparseMatrixCSR{$elty}(csc::CuSparseMatrixCSC{$elty}; index::SparseChar='O', action::cusparseAction_t=CUSPARSE_ACTION_NUMERIC, algo::cusparseCsr2CscAlg_t=CUSPARSE_CSR2CSC_ALG1)
             m,n    = size(csc)
-            rowPtr = CUDA.zeros(Cint,m+1)
+            rowPtr = CUDA.ones(Cint,m+1)
             colVal = CUDA.zeros(Cint,nnz(csc))
             nzVal  = CUDA.zeros($elty,nnz(csc))
             function bufferSize()
@@ -375,7 +375,7 @@ for (elty, welty) in ((:Float16, :Float32),
     @eval begin
         function CuSparseMatrixCSC{$elty}(csr::CuSparseMatrixCSR{$elty}; index::SparseChar='O', action::cusparseAction_t=CUSPARSE_ACTION_NUMERIC, algo::cusparseCsr2CscAlg_t=CUSPARSE_CSR2CSC_ALG1)
             m,n = size(csr)
-            colPtr = CUDA.zeros(Cint, n+1)
+            colPtr = CUDA.ones(Cint, n+1)
             rowVal = CUDA.zeros(Cint, nnz(csr))
             nzVal = CUDA.zeros($elty, nnz(csr))
             if $elty == Float16 #broken for ComplexF16?
@@ -401,7 +401,7 @@ for (elty, welty) in ((:Float16, :Float32),
 
         function CuSparseMatrixCSR{$elty}(csc::CuSparseMatrixCSC{$elty}; index::SparseChar='O', action::cusparseAction_t=CUSPARSE_ACTION_NUMERIC, algo::cusparseCsr2CscAlg_t=CUSPARSE_CSR2CSC_ALG1)
             m,n    = size(csc)
-            rowPtr = CUDA.zeros(Cint,m+1)
+            rowPtr = CUDA.ones(Cint,m+1)
             colVal = CUDA.zeros(Cint,nnz(csc))
             nzVal  = CUDA.zeros($elty,nnz(csc))
             if $elty == Float16 #broken for ComplexF16?
@@ -490,7 +490,7 @@ for (fname,elty) in ((:cusparseScsr2bsr, :Float32),
             nnz_ref = Ref{Cint}(1)
             mb = cld(m, blockDim)
             nb = cld(n, blockDim)
-            bsrRowPtr = CUDA.zeros(Cint,mb + 1)
+            bsrRowPtr = CUDA.ones(Cint,mb + 1)
             cudesca = CuMatrixDescriptor('G', 'L', 'N', index)
             cudescc = CuMatrixDescriptor('G', 'L', 'N', indc)
             cusparseXcsr2bsrNnz(handle(), dir, m, n, cudesca, csr.rowPtr,
@@ -519,7 +519,7 @@ for (fname,elty) in ((:cusparseSbsr2csr, :Float32),
             nb = cld(n, bsr.blockDim)
             cudesca = CuMatrixDescriptor('G', 'L', 'N', index)
             cudescc = CuMatrixDescriptor('G', 'L', 'N', indc)
-            csrRowPtr = CUDA.zeros(Cint, m + 1)
+            csrRowPtr = CUDA.ones(Cint, m + 1)
             csrColInd = CUDA.zeros(Cint, nnz(bsr))
             csrNzVal  = CUDA.zeros($elty, nnz(bsr))
             $fname(handle(), bsr.dir, mb, nb,
diff --git a/lib/cusparse/generic.jl b/lib/cusparse/generic.jl
index e944645760..7280ef4c23 100644
--- a/lib/cusparse/generic.jl
+++ b/lib/cusparse/generic.jl
@@ -69,6 +69,13 @@ function densetosparse(A::CuMatrix{T}, fmt::Symbol, index::SparseChar, algo::cus
         end
         cusparseDenseToSparse_convert(handle(), desc_dense, desc_sparse, algo, buffer)
     end
+    # Issue with the CUDA routine `cusparseDenseToSparse_convert`
+    if (index == 'O') && (fmt == :csc) && (n == 0)
+        B.colPtr = CuVector{Cint}([1])
+    end
+    if (index == 'O') && (fmt == :csr) && (m == 0)
+        B.rowPtr = CuVector{Cint}([1])
+    end
     return B
 end
 
diff --git a/test/libraries/cusparse/conversions.jl b/test/libraries/cusparse/conversions.jl
index 1a5119f289..9b34aefd9c 100644
--- a/test/libraries/cusparse/conversions.jl
+++ b/test/libraries/cusparse/conversions.jl
@@ -10,7 +10,7 @@ using CUDA
     J = [2,3,4] |> cu
     V = Float32[1,2,3] |> cu
 
-    dense = rand(3,3) |> cu
+    dense = rand(Float32, 3,3) |> cu
 
     # check defaults
     @test sparse(I, J, V) isa CuSparseMatrixCSC
@@ -39,6 +39,54 @@ using CUDA
     end
 end
 
+@testset "sparse -- empty matrix" begin
+    n, m = 0, 0
+    I = [] |> cu
+    J = [] |> cu
+    V = Float64[] |> cu
+
+    dense = rand(m,n) |> cu
+
+    # check defaults
+    @test sparse(I, J, V) isa CuSparseMatrixCSC
+    @test sparse(dense) isa CuSparseMatrixCSC
+
+    for (fmt, T) in  [(:coo, CuSparseMatrixCOO),
+                      (:csc, CuSparseMatrixCSC),
+                      (:csr, CuSparseMatrixCSR),
+                      (:bsr, CuSparseMatrixBSR)
+                     ]
+        @testset "sparse $T" begin
+            if fmt != :bsr # bsr not supported
+                x = sparse(I, J, V; fmt=fmt)
+                @test x isa T{Float64}
+                @test size(x) == (0, 0)
+
+                x = sparse(I, J, V, m, n; fmt=fmt)
+                @test x isa T{Float64}
+                @test  size(x) == (0, 0)
+
+                if fmt == :csc
+                    @test collect(x.colPtr) == [1]
+                end
+                if fmt == :csr
+                    @test collect(x.rowPtr) == [1]
+                end
+            end
+
+            x = sparse(dense; fmt=fmt)
+            @test x isa T{Float64}
+            @test collect(x) == collect(dense)
+            if fmt == :csc
+                @test collect(x.colPtr) == [1]
+            end
+            if fmt == :csr
+                @test collect(x.rowPtr) == [1]
+            end
+        end
+    end
+end
+
 @testset "unsorted sparse (CUDA.jl#1407)" begin
     I = [1, 1, 2, 3, 3, 4, 5, 4, 6, 4, 5, 6, 6, 6]
     J = [4, 6, 4, 5, 6, 6, 6, 1, 1, 2, 3, 3, 4, 5]