Abstract: Flexible job shop has gradually become an important carrier to cope with the complex manufacturing demand due to its efficient allocation of production resources and dynamic adjustment ability. The flexible job shop scheduling problem (FJSP) with batch processing machines extends the traditional flexible job shop by incorporating key equipment as batch processing machines, adapting it to realistic multi-variety production with varying batch sizes, and has important research and application value. Comprehensively considering the batch processing characteristics that may exist in actual production, as well as the scheduling requirements for parallel and serial batch processing operations. The lot-streaming flexible job shop scheduling problem with hybrid batch processing machines is studied in this paper. A detailed description of this scheduling problem has been provided. A three-layer chromosome encoding scheme combined with a hybrid selective insertion-based decoding method is designed based on the problem characteristics. For the sublot size encoding, a corresponding crossover operator and three mutation operators are proposed, along with a repair mechanism for process encoding after crossover and mutation. Finally, a two-stage genetic algorithm is developed to solve the problem, and its effectiveness is validated on randomly generated instances.