Spatial domain-decomposing is applicable for solving the neutron transport equation on massively parallel architectures. However, the more sub-domains there are, the slower the convergence is. Then CMFD is used to accelerate the spatial domain-decomposed parallel MOC in order to overcome the problem. The CMFD coarse diffusion equation is solved by ScaLAPACK, and the CMFD results are used to update both fine-mesh scalar fluxes and inner-interface angular fluxes. Numerical results on 1D slab example illustrate that CMFD is an efficient acceleration method for the spatial domain-decomposed parallel MOC, which improves the convergence remarkably.