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Flexible job shop scheduling problem (FJSP) is a research hotspot of job shop scheduling problems (JSPs). JSP has been proved to be NP-hard, yet the computational complexity of FJSP is much higher, which disables exact solution methods and makes heuristic approaches more qualified. In this paper, a kind of FJSP is analyzed and formulated, which considers storing and maintaining costs of operations finished ahead of schedule, compensation fees of delayed jobs, and the requirement of evenly allocating workloads among machines. A particle swarm optimization algorithm (PSO) based on a swarm grouping mechanism is proposed for this FJSP problem. The algorithm partitions the swarm into many groups, and each group flies toward its own global best particle. Adopting the swarm grouping mechanism, the algorithm avoids of being premature. Feasibility and efficiency of the algorithm are verified through numerical experiments by comparing it with genetic algorithm (GA) and standard PSO.