Finite volume method(FVM) is now a popular fluid dynamics computational method in scientific and engineering research. Diffusion equation describes a large kind of transportation for mass, energy, momentum and son on. Diffusion term is the important one in diffusion and convection equation and in the Navier-stokes equations. For engineering process computations, unstructured mesh may be a good choice for it can satisfy complex domain gridding. But the cross-diffusion term generated in the discretization of diffusion term has much effect on the convergence and accuracy. In this paper an improved finite volume scheme to discretize diffusive flux on a nonorthogonal mesh is proposed. Using a modified decomposition of the normal gradient as Xue and Barton, the flux formula was derived. The most important point of our scheme is that, unlike classical schemes on unstructured mesh for diffusion flux, there are no cross-diffusion term need deferred correction, so the convergence rate may be accelerated. The performances of both schemes are compared for a Poisson problem solved in square domains where control volumes are increasingly skewed in order to test their robustness and efficiency. It is shown that convergence properties and the accuracy order of the solution are degraded on extremely skewed mesh. Then, the very stable behavior of the method is successfully demonstrated on a randomly distorted grid. It was shown the convergence rate and accuracy of this scheme is almost grid skewness independent.