For the flexible job shop scheduling problem (FJSP), in order to optimize the maximum completion time, a hybrid algorithm mixed with bilevel neighborhood search and genetic algorithm is proposed. The neighborhood structure is constructed by using machine idle time to reduce the maximum completion time. In order to improve the current solution, critical operations of the critical path are moved to achieve neighborhood search. The method of bilevel neighborhood search is designed according to the characteristics of FJSP. The first level neighborhood search is the cross-machine moving operation, and the operation is moved to other optional machines in addition to current processing machine. The second level neighborhood search is the same-machine moving operation, and the operation is moved on current processing machine. Operation moving conditions corresponding to the bilevel neighborhood search are given to ensure feasible solutions. Both of global search ability and local search ability of FJSP solving algorithm are considered, and to use genetic algorithm to achieve global search, bilevel neighborhood search to achieve local search. The internationally accepted FJSP benchmark examples are adopted to test the validity of the proposed method.