In this study, the convergence rates of the two one-node CMFDs were evaluated for the sequential and the parallel algorithm. The results from the Fourier analyses and the numerical simulations showed good agreement, except for the parallel algorithm in optically thin region as an effect of boundary condition is appeared. The one-node CMFD showed instabilities in both sequential and the parallel algorithm with large scattering ratio. On the other hand, the one-node pCMFD was everywhere stable according to this study. From this result, the one-node pCMFD was found to be a better option for the parallel algorithm.