Abstract: Backdoor is one of these structures,which can effectively improve the efficiency of the SAT problem solving,and which become a focus of study in recent years.The variable assignment for backdoors can reduce the search branch of SAT problem solving process effectively,thereby reducing the time complexity and space complexity of sat problem solver.In order to improve the efficiency of the SAT problem,this paper presents the improved algorithm of backdoor sets for sloving SAT problem,and provides the definition of the smallest backdoor sets.The heuristic is joined in this algorithm,so the smaller backdoor sets can be solved in this way,Finally,this paper proposed summary and outlook.