Aiming at the multi-objective unrelated parallel machine hybrid flow shop scheduling problem， a multi-objective mathematical model with the goal of minimizing the maximum completion time， the total energy consumption of the machine and the processing cost of the machine is established. An improved multi-objective evolution algorithm based on decomposition（IMOEAD） is proposed. The uniform design table is used to generate the initial weight vector to improve the population diversity. The normal distribution is used to cross and design an adaptive Gaussian mutation to improve the global search ability and local search ability of the algorithm. Individuals are selected in the weight vector neighborhood to generate new solutions， and non-dominated levels and crowding distances are used to update external files. Inverted generational distance （IGD）， generational distance （GD） and number of non-dominated solutions （NDS） are taken as performance indicators. Through simulation cases， the effectiveness of IMOEAD is verified compared with non-dominated sorting genetic algorithm Ⅱ （NSGA-Ⅱ） and multi-objective evolution algorithm based on decomposition （MOEA/D）.