In this paper，the basis of the combined finite and discrete element method (FEM/DEM) is introduced，and an adaptive Slave region method is proposed according to the FEM/DEM simulation of tire-sand interactions． Moreover，the three-dimension simulation models of tires running on sand are constructed based on a soil bin experiment with the tire deformation being neglected，where the sand is modeled by using spherical discrete elements，the soil bin and the tires are discretized into hexahedron finite elements． Then，the running behaviors of the smooth and groove tires on sand at different slip ratios are simulated by using the self-developed software CDFP，which is an explicit combined discrete-finite element program． The simulation results of the smooth tire are compared with the corresponding experimental ones，thus verifying the feasibility and effectiveness of the proposed method． In addition，the comparison of the simulation results (such as road reaction force and tire drawbar pull) of the smooth and groove tires explains the necessity of the grooves of off-road vehicle tires．