PSTD (pseudospectral time domain) is recognized as one of the powerful models to accurately calculate the scattering properties of nonspherical particles. But it is only good at the computation in coarse spatial resolution, and large "staircase approximation error" will occur in the actual computation. To solve this problem, the variable dimension scheme is introduced to improve the PSTD computation, in which, the finer grid cells are set near the particle's surface. In order to ensure that the PSTD algorithm can be performed on non-uniform grids, we have improved the PSTD with the space mapping technique so that the FFT algorithm can be implemented. The performance of the improved PSTD (called "IPSTD" in this paper) is investigated from two aspects: for the calculation accuracy, the phase matrices calculated by IPSTD are compared with those well tested scattering models like Lorenz-Mie theory, T-matrix method and DDSCAT; for computational efficiency, the computational time of PSTD and IPSTD are compared for the spheres with different sizes. From the results, it can be found that, the IPSTD scheme can improve the simulation accuracy of phase matrix elements notably, especially in the large scattering angles; though the computational burden of IPSTD is larger than that of PSTD, its computational burden does not increase substantially.