This article presents the convergence analysis of the coarse mesh finite difference (CMFD) method applied to two-group (2-G) three-dimensional (3D) neutron diffusion problem. Two CMFD algorithms are examined: one-node (1-N) CMFD and two-node (2-N) CMFD. Two test problems are used for the study of the convergence behavior: a model problem of homogeneous 2-G 3D eigenvalue problem and the NEACRP LWR transient benchmark problem. The convergence rates of the 1-N and 2-N CMFD algorithms are numerically measured in terms of the convergence of current correction factors (CCFs). The numerical test results are presented as well as the comparison with the previous analytical study. Overall, 1-N CMFD with the CCF relaxation shows a comparable performance to 2-N CMFD for the realistic 3D rod ejection transients.