One mission of on-orbit servicing can be fulfilled in many ways, and proper mission assignment must be guaranteed. In light of this, first, the reachable domain of service spacecraft was resolved and the target spacecraft which satisfies the reachable domain was filtered. Then the assignment of servicing based on the optimization of multi-objective, including time, fuel consumption and priority, was studied. The best plan was achieved by building the model of 0-1 integer programming and taking the NSGA-Ⅱ algorithm with the constraint of time and fuel consumption. Finally two examples of simulation were given, one demonstrating the general results of the above method, either compared with another algorithm. The simulation results indicate that the above method is effective in solving the problem of mission assignment for on-orbit servicing.