Abstract: Aiming at the hybrid job-shop scheduling with multiprocessor task (HJSMT) problem, a green HJSMT problem model is established to minimize the maximum completion time and total energy cost, and an improved equilibrium optimizer (IEO) algorithm is proposed to solve the problem. In the initialization stage, the algorithm adopts the mixed population strategy and integrates the random generation and chaotic mapping rules to improve the diversity and quality of the initial solution set. In the global search phase, Lévy flight strategy and reverse search strategy are introduced to effectively expand the search range and help the population jump out of the local optimal. In addition, the local search based on simulated annealing is introduced to enhance the local search ability of the algorithm and reduce the risk of the population falling into local optimal. A large number of simulation experiments are used to verify the performance of the proposed algorithm. The experimental results show that compared with other comparison algorithms, IEO shows stronger superiority and stability in the optimization of green HJSMT problems.