A difference scheme for diffusion equation on Voronoi meshes is constructed using finite volume method.The diffusion discretization scheme is simpler on Voronoi meshes than on quadrilateral meshes.It introduce no cell-node unknown and improves accuracy of the discrete calculation of cell-edge flux as well as accuracy of difference scheme.The diffusion calculation on Voronoi meshes can be coupled with cell-centered hydrodynamics calculations.Computation examples demonstrate that the accuracy on Voronoi meshes is higher than that on quadrilateral meshes and Voronoi meshes adapt well to distortion.