As for the thin-walled parts of the aircraft in the assembly stage, high-precision finishing is required to meet the assembly accuracy requirements. In order to ensure accurate machining paths and allowance, it is necessary to register the parts with mutual assembly relationships. This paper proposes an algorithm for surface registration of aircraft parts assembly based on multiple constraints. First, according to the actual assembly situation of the parts, three constraint criteria are proposed and converted into the corresponding objective function; then the parameters to be sought in the objective function are differentiated and the feasible solution of the parameters to be sought is obtained through the alternate gradient descent algorithm. Experimental verification shows that the method in this paper can accurately register the point clouds of different poses of the mating surface of the part. Based on the registration result, accurate machining path and allowance can be obtained, which lead to better part assembly quality.