A mathematical model aiming at minimizing the makespan, total machine utilization and energy consumption is established according to the multi-objective flexible job shop green scheduling problem(MO-FJGSP). A self-adaptive multi-objective Jaya algorithm(SAMO-Jaya) based on Pareto optimal solution is designed to optimize the model. And two-level real number encoding is adopted to implement the coding scheme of processes' sequences and machines' assignment, then a transformation mechanism is designed to create a mapping between the continuous solution space of Jaya and the discrete solution space of flexible job-shop scheduling problem(FJSP). And then a hybrid strategy combining chaotic sequence and uniform distribution is raised to improve the quality and diversity of the initial populations. In addition, a self-adaptive population size adjusting method is embedded to improve the optimizing speed of the algorithm. By analyzing the solutions of 10 single-objective benchmarks and 3 multi-objective benchmarks solved by SAMO-Jaya and other 7 existing algorithms, the results show that SAMO-Jaya can solve the MO-FJGSP effectively.