Belief propagation algorithm is very effective in finding satisfying assignments for RB(k,n,α,r_c,p) model instances where hard region becomes narrower. However, belief propagation algorithm does not always converge for factor graphs with cycles. Unfortunately, rigorous theoretical proof of this phenomenon is still lacking. Belief propagation algorithm is the most basic message passing algorithms. This study derives the convergence conditions of the belief propagation algorithm for solving RB(k,n,α,r_c,p) model instances. In the RB(k,n,α,r_c,p) model with k=2, α>（1/k）， r_c>0 and which proves that BP will be converged with high probability if p∈(0,n^-2α). Experimental results show that such convergence conditions of belief propagation algorithm are very effective in two different group data from the random RB(k,n,α,r_c,p) model instances. In the RB(k,n,α,r_c,p) model, when n increases, the experimental convergence interval is fixed range, while the theory convergence interval become narrower. It is because the number of incompatible assignment are determined by n and p in the RB(k,n,α,r_c,p).