The CMFD and p-CMFD acceleration schemes have been comparatively investigated in view of the Monte Carlo simulation. In terms of the FSD convergence, both CMFD and p-CMFD are very effective and comparable. However, the multi-cycle accumulation of the MC quantities is necessary for stable implementation of the conventional CMFD scheme, while the p-CMFD is always stable. Regarding the variance reduction, MC run with both CMFD and p-CMFD shows the smaller real-to-apparent variance. It is also mentioned that the p-CMFD reduces the variance more effectively than CMFD. In the future, further in-depth comparison will be conducted for the two CMFD schemes in a continuous energy MC platform.