In the many-objective optimization algorithms, maintaining a balance between convergence and diversity is critical to overall performance. However, a single dominance relation often proves insufficient in preserving this balance. To address this challenge, a many-objective evolutionary algorithm based on adaptive dominance strategy (ADSMOEA) is proposed. The adaptive dominance strategy integrates two complementary dominance relations. One dominance relation focuses on convergence, while the other focuses on diversity. The strategy selects the most appropriate relation based on the current state of the population, which ensures the balance between convergence and diversity. Furthermore, to accurately assess the convergence state of the population, an angle convergence indicator is designed to enhances the precision of convergence evaluation by incorporating information regarding the angles between objective vectors. This improvement provides reliable guidance for the selection of the dominance relation. In addition, an adaptive diversity operator is designed to maintain population diversity. To validate the effectiveness of the ADSMOEA, we conduct comparative simulations experiments between the proposed algorithm and seven state-of-the-art algorithms. The results show that the proposed ADSMOEA exhibits strong competitiveness in solving many-objective optimization problems.