To solve the multi-objective flexible job-shop problem (MFJSP), an effective Pareto-based estimation of distribution algorithm (P-EDA) is proposed. The fitness evaluation based on Pareto optimality is employed and a probability model is built with the Pareto superior individuals for estimating the probability distribution of the solution space. In addition, a mechanism to update the probability model is proposed, and the new individuals are generated by sampling the promising searching region based on the probability model. To avoid premature convergence and enhance local exploitation, the population is divided into two sub-populations at certain generations according to a splitting criterion, and different operators are designed for the two sub-populations to generate the promising neighbour individuals. Moreover, multiple strategies are utilised in a combination way to generate the initial solutions, and a local search strategy based on critical path is proposed to enhance the exploitation ability. Furthermore, the influence of parameters is investigated based on the Taguchi method of design of experiment, and a suitable parameter setting is suggested. Finally, numerical simulation based on some well-known benchmark instances and comparisons with some existing algorithms are carried out. The comparative results demonstrate the effectiveness of the proposed P-EDA in solving the MFJSP.