Abstract: In this paper, two numerical schemes were developed for both two-dimensional temporally and two-dimensional spatially fractional advection-dispersion equations and their numerical solutions were achieved. We analyzed the variation of diffusion with the fractional order by applying the numerical scheme in a test case and verified the temporal and spatial correlation. Then we compared the calculation results of our new schemes with the solution of traditional two-dimensional advection-dispersion equation. When the fractional orders are integer, the calculation results of both two-dimensional temporally and two-dimensional spatially fractional advection-dispersion equations are the same as that of the traditional integer order advection-dispersion equation. These indicate that the numerical schemes for the two-dimensional fractional advection-dispersion equations developed in this paper are feasible.