Structured mesh with local adaptive refinement techniques (SAMR) are widely used in scientific computation.The SAMR mesh consists of a hierarchy of refinement levels, each level is uniform and organized as a union of rectangular patches.The finer level is constructed by refining the coarser level locally.On SAMR hierarchy.mesh, time integration usually advancing with two strategies, refinement advancing and composite advancing.Refinement advancing is a recursive process, i.e.each level advancing followed by the finer level advancing with the temporal refinement strategy.When the finer level reached the time corresponding to the end of the coarser level, a synchronization process is required to correct the flux mismatches at the coarse-fine interface.In composite advancing strategy, all levels are combined into a composite mesh, time integration advancing on the composite mesh.Refinement advancing strategy has many advantages both for algorithm designing and parallel implementation.However, Refinement advancing strategy is originally developed to solve the hyperbolic equations with explicit integration.In this presentation, we consider the solution for diffusion equations on SAMR hierarchy mesh.An implicit time-integration algorithm with refinement advancing is presented.In order to show its efficiency, the algorithm is applied to the radiation hydrodynamics simulation, where the solution of non-equilibrium radiation diffusion equations is required.Based on a parallel software infrastructure JASMIN[1], simulation results on thousands of CPU cores are given.