Message propagation algorithms are very effective in finding satisfying assignments for SAT instances, and hard region become narrower. However, message propagation algorithms do not always converge for graphs with cycles. Unfortunately, rigorous theory proof of this phenomenon is still lacking. Warning propagation (WP) algorithm is the most basic message propagation algorithm, we have derived the sufficient conditions for convergence of the warning propagation algorithm. Lastly, experimental results show that such conditions for convergence of WP are very effective in different group data from random satisfiable 3-SAT instances.