Diffusion of self-propelled particles in the presence of randomly distributed obstacles is studied in three dimensions (3D) using Langevin dynamics simulations. It is found that depending on the magnitude of the propelling force and the particle aspect ratio, the diffusion coefficient can be a monotonically decreasing or a non-monotonic concave function of the obstructed volume fraction. Counterintuitive enhancement of the particle diffusivity with increasing the obstacle crowd is shown to be resulted from interplay of self-propulsion and anisotropy in the particle shape. On the propelling force-aspect ratio plane, regions that correspond to monotonic and non-monotonic dependence of the diffusivity on obstacle density are specified using the simulation results and the boundary between the two regions is described.