For high efficiency simulation of three-dimensional spherical implosion and the difficulty of adding radiation source on traditional Cartesian orthogonal grid, a multi-block non-orthogonal mesh generation method is developed. An efficient parallel algorithm of three-dimensional diffusion scheme on these meshes is proposed. It was applied to the simulation of radiation hydrodynamic equations and the asymmetry study in three-dimensional implosion problems. Effectiveness of the algorithm is shown. Scalability is demonstrated with a parallel efficiency above 69% on 5400 processors.