In this paper, an algorithm based on heuristic function for minimum set-covering problem is presented, as well as the definition of complete strategy concept and the method to structure heuristic function. The rationality, the time complexity and the precision of the solution are discussed for the algorithm. The basic idea is to structure heuristic function with the given heuristic strategies. The method can apply to other NP hard problems. As application of the algorithm, this paper presents a new algorithm of learning rule from the examples based on heuristic function.