In order to improve the reliability and accuracy of Monte Carlo program in the critical safety calculation of loosely coupled systems, an improved Shannon entropy diagnose method considering the distribution of fission sources and the statistical bias is proposed in this paper. The relative deviation of the distribution of fission sources between adjacent generations and the standard deviation of fission source is proposed. The standard deviation of fission source distribution during source iteration are used as the weight of fission source distribution. Finally, an improved Shannon entropy diagnose method considering the distribution of fission sources and the statistical bias is proposed. This improved Shannon entropy convergence index makes up for the shortcomings of traditional Shannon entropy for lacking the details of local fission source. The improved Shannon entropy convergence index is applied to the benchmark problem: loosely coupled solution Slabs. The results show that compared with the traditional Shannon entropy index, this improved Shannon entropy is more sensitive to the iterative convergence process and can more intuitively and accurately determine the convergence of fission source distribution accompanied by source iteration.