Much effort has been made to solve computing problems by using DNA-an organic simulating method, which in some cases is preferable to the current electronic computer. However, No one at present has proposed an effective and applicable method to solve addition problem with molecular algorithm due to the difficulty in solving the carry problem which can be easily solved by hardware of an electronic computer. In this article, we solved this problem by employing two kinds of DNA strings, one is called result and operation string while the other is named carrier. The result and operation string contains some carry information by its own and denotes the ultimate result while the carrier is just for carrying use. The significance of this algorithm is the original code, the fairly easy steps to follow and the feasibility under current molecular biological technology.