In order to solve the flexible job shop scheduling problem with multi-objectives and multi-constraints, a state transition algorithm based on normal cloud models is proposed. A mathematical model of multi-objective flexible job shop scheduling problems with the goal of minimizing the maximum completion time, total workload and bottleneck machine workload is constructed, and an adaptive value allocation strategy to improve the grey entropy correlation degree is proposed, which can not guide the evolution of the algorithm when the difference between the Pareto solution comparison sequence and the reference sequence is equal using the fitness allocation strategy of grey entropy correlation degree. At the same time, the cloud model evolution strategy with both fuzziness and randomness is introduced to improve the state transition algorithm, which can effectively avoid the precocious of the algorithm and increase the diversity of candidate solutions. The simulation results show that the state transition algorithm based on normal cloud models can effectively solve the multi-objective flexible job shop scheduling problem, and compared with other algorithms, this algorithm has higher convergence accuracy and faster convergence speed.