The three-dimensional (3D) dynamics of a projectile in granular media is simulated using DEM (discrete element method). Periodic boundary conditions are adopted, and the effects of gravity, contact forces, damping and friction are taken into account. The 3D simulation results fit the experiment results very well. Simulation results show that the heaver the projectile, the deeper the penetration depth. The impact depth grows linearly when the projectile quality increases. And when the density of granular media decreases, the penetration depth also increases. Splash of granular particles is also observed in the impact simulation.