Most of multi-objective evolutionary algorithms (MOEAs) in the literature are based on Pareto ranking. They are successful in solving many bi-objective or three-objective optimization problems, but their performance will deteriorate quickly as the number of objectives increases. In order to address this problem, the algorithm developed in this paper aims to find a satisfying solution among Pareto optimal set by an improved average ranking method, which can compare and rank all individual solutions, including non-dominated ones. Hence, its performance is not affected by the number of objectives. As the effectiveness of average ranking depends on the distribution of individuals in the population, a chaotic map model is designed and used to initialize the population periodically so as to keep the population diversity. The experimental study shows that the proposed MOEA based on average ranking outperforms a state-of-the-art MOEA based on Pareto ranking in terms of both the convergence accuracy and the run time on a set of benchmark test problems.