Aiming at the Pareto optimal problem for multi-objective flow shop scheduling, this study builds a multi-objective flow shop scheduling problem model with maximum completion time and maximum delay time as the optimization objectives. Meanwhile, the study designs a genetic reinforcement learning algorithm based on Q-learning for the Pareto optimal solution of the problem. The algorithm introduces state variables and action variables and obtains the initial population by Q-learning algorithm to improve the initial solution quality. During the evolution of the algorithm, the Q-table is applied to guide the mutation operation to expand the local search range. The Pareto fast non-dominated sorting and congestion calculation are adopted to improve the solution quality and diversity, and the Pareto optimal solution is obtained step by step. The effectiveness of the improved genetic enhancement algorithm for the Pareto optimal solution of the multi-objective flow shop scheduling problem is verified by comparing the proposed algorithm with the genetic algorithm, NSGA-II algorithm, and Q-learning algorithm.