This paper proposes a Pareto-based grouping discrete harmony search algorithm (PGDHS) to solve the multi-objective flexible job shop scheduling problem (FJSP). Two objectives, namely the maximum completion time (makespan) and the mean of earliness and tardiness, are considered simultaneously. Firstly, two novel heuristics and several existing heuristics are employed to initialize the harmony memory. Secondly, multiple harmony generation strategies are proposed to improve the performance of harmony search algorithm. The operation sequence in a new harmony is produced based on the encoding method and the characteristics of FJSP. Thirdly, two local search methods based on critical path and due date are embedded to enhance the exploitation capability. Finally, extensive computational experiments are carried out using well-known benchmark instances. Three widely used performance measures, number of non-dominated solutions, diversification metric and quality metric, are employed to test the performance of PGDHS algorithm. Computational results and comparisons show the efficiency and effectiveness of the proposed PGDHS algorithm for solving multi-objective flexible job-shop scheduling problem.