Molecular dynamics simulations have been performed to investigate the transport properties of self-diffusion coefficients in the penetrable-sphere model system. The resulting simulation data for the product of the packing fraction and the self-diffusion coefficient exhibit a transition from an increasing function of density in lower repulsive systems, where the soft-type collisions are dominant, to a decreasing function in higher repulsive systems, where most particle collisions are the hard-type reflections due to the low-penetrability effects. A modified Enskog-like equation implemented by the effective packing fraction with the mean-field energy correction is also proposed, and this heuristic approximation yields a reasonably good result even in systems of high densities and high repulsive energy barriers.