Belief propagation (BP) algorithm is a message passing algorithm based on a factor graph, and it passes messages from one node to another through edges in the graph to determine the value of some variables with high probability. This method is experimentally proven to be very effective when solving the satisfiability (SAT) problem. However, there is no explanation for its effectiveness from a theoretical point of view at present. Through the analysis of convergence of the BP algorithm, the effectiveness of the algorithm is explained theoretically. In this study, the sufficient conditions are also derived for convergence of the BP for satisfiability problem, and extending message (0,1) to message (-∞,+∞). Lastly, experimental results show that the conditions for convergence of BP are very effective in random SAT instances, and it proves the correctness of the conclusion.