A simple and e ective numerical method is proposed for simulating the temporal di usive mass transport process through a microstructure with arbitrary complexity described by a phase-®eld approach. The mass di usion through a given microstructure is modeled by a di usion equation with a variable di usion coe cient, which is solved by an e cient and accurate semi-implicit spectral method. It is shown that it is possible to extract the e ective di usion coe cient for any given microstructure from the temporal concentration pro®les. The method is used to simulate the grain boundary di usion in a single-phase polycrystalline grain structure and the heterogeneous di usion in a twophase microstructure with di erent di usion coe cient in each phase. Results are compared with existing analytical theories and computer simulations. Ó