In order to avoid calculation bias and increase calculation efficiency, convergence of the fission source distribution (FSD) in Monte Carlo simulations is important. Numerous analysis methods have been developed and used for checking the fission source convergence. However, such schemes have low applicability to Monte Carlo codes or give low diagnostic accuracy. To address these limitations, a method to verify the fission source convergence using the average and standard deviation of fission source positions is proposed. To collect the fission site information, the MCNP5 code was modified, and position information was extracted. The accuracy and advantages of the proposed method were verified by solving Organisation for Economic Co-operation and Development/Nuclear Energy Agency benchmark problems with the modified MCNP5 code and comparing the results to those obtained with the Shannon entropy and the nine center distance sum approaches. The analysis shows that the proposed method has good applicability and exhibits high accuracy for verifying the convergence of the FSD. It is expected that the proposed scheme will be a valuable contribution to the field of the fission source convergence.