We introduce a new algorithm for subset sum problem. For any given problem with A(1)，A(2)，…，A(n-1)，A(n),and M, the time complexity of the algorithm is O(n^log₂^(M+1)+1)and the space complexity is O(n), where A(1)，A(2)，…，A(n-1)，A(n),and M are all positive integers. This result is better than that of the two-list algorithm when M is relatively small.