Multiobjective evolutionary algorithms have become prevalent and efficient approaches for solving multiobjective optimization problems. However, their performances deteriorate severely when handling many-objective optimization problems (MaOPs) due to the loss of selection pressure to drive the search toward the Pareto front and the ineffective design in diversity maintenance mechanism. This paper proposes a many-objective evolutionary algorithm (MaOEA) based on directional diversity (DD) and favorable convergence (FC). The main features are the enhancement of two selection schemes to facilitate both convergence and diversity. In the algorithm, a mating selection based on FC is applied to strengthen selection pressure while an environmental selection based on DD and FC is designed to balance diversity and convergence. The proposed algorithm is tested on 64 instances of 16 MaOPs with diverse characteristics and compared with seven state-of-the-art algorithms. Experimental results show that the proposed MaOEA performs competitively with respect to chosen state-of-the-art designs.