This paper presents an adaptive epsilon non-dominated sorting method for multi-objective evolutionary optimization which has the ability to preserve both the efficiency and diversity. In NSGA-II, a fast non-dominated sorting mechanism is applied to sort solutions in an efficient way. However, it may suffer from deterioration and diversity in population is not as great as expected. To solve this problem, the concept of epsilon-dominance is applied for updating solutions in non-dominate sorted layers according to adaptive epsilon value, and the novel update strategy could prevent deterioration and keep diversity well. A real-world city map with 410 nodes and 1334 arcs is used in experiment, and the result shows that the proposed algorithm (AENSGA) performs better than NSGA-II in multi-objective shortest path problem.