［Purposes］For solving multiobjective optimization problems more efficiently, a more effective Pareto frontier is obtained. ［Methods］By introducing the nonmonotone Armijo criterion, a new step-size search method is obtained, and then a nonmonotone diagonal steepest descent algorithm for multi-objective optimization problems is proposed. ［Findings］Under the assumptions of non-convexity of the objective function, gradient Lipschitz continuity and lower boundedness, it is proved that each accumulation point of the sequence generated by the algorithm is a Pareto weak efficient solution of the multiobjective optimization problem, and the sublinear convergence of the algorithm is proved under appropriate conditions. ［Conclusions］Numerical experiments show that the average value of the objective function value of the proposed algorithm is smaller.