A discrete particle swarm optimization algorithm with adaptive inertia weight (DPSO-AIW) is proposed to solve the multiobjective Flexible Job-shop Scheduling Problem. The algorithm uses a two-layer coding structure to encode the chromosomes, namely operation sequence (OS) and machine assignment (MA). The initial population combined random selection of OS and the global selection based on operation (GSO) of MA. In order to obtain the Pareto optimal solution, non-dominated fronts are obtained by rapid non-dominated sorting. In the evolution process, the discrete particle swarm optimization algorithm is used to directly solve the values of the next generation chromosomes in the discrete domain, and the population diversity is enhanced by adaptively adjusting the variation of the inertia weight ω, and the Pareto optimal solution obtained in the process is stored in the Pareto optimal solution set (POS). Finally, numerical simulation based on two sets of international standard instances and comparisons with some existing algorithms are carried out. The comparative results demonstrate the effectiveness and practicability of the proposed DPSO-AIW in solving the multiobjective Flexible Job-shop Scheduling Problem.