Balancing population diversity and convergence is critical for evolutionary algorithms to solve many-objective optimization problems (MaOPs). In this paper, a two-round environmental selection strategy is proposed to pursue good tradeoff between population diversity and convergence for many-objective evolutionary algorithms (MaOEAs). Particularly, in the first round, the solutions with small neighborhood density are picked out to form a candidate pool, where the neighborhood density of a solution is calculated based on a novel adaptive position transformation strategy. In the second round, the best solution in terms of convergence is selected from the candidate pool and inserted into the next generation. The procedure is repeated until a new population is generated. The two-round selection strategy is embedded into an MaOEA framework and the resulting algorithm, namely, 2REA, is compared with eight state-of-the-art MaOEAs on various benchmark MaOPs. The experimental results show that 2REA is very competitive with the compared MaOEAs and the two-round selection strategy works well on balancing population diversity and convergence.