Unlike the considerable research on solving many objective optimization problems with evolutionary algorithms, there has been much less research on constrained many-objective optimization problems (CMaOPs). Generally, to effectively solve CMaOPs, an algorithm needs to balance feasibility, convergence, and diversity simultaneously. It is essential for handling CMaOPs yet most of the existing research encounters difficulties. This paper proposes a novel constrained many-objective optimization evolutionary algorithm with enhanced mating and environmental selections, namely CMME. The main features are: i) two ranking strategies are proposed and applied in the mating and environmental selections to enrich feasibility and convergence; ii) an individual density estimation is designed, and crowding distance is integrated to promote diversity; and iii) the ?-dominance is used to strengthen the selection pressure on both the convergence and diversity. The synergy of these components can achieve the goal of balancing feasibility, convergence, and diversity for solving CMaOPs. The proposed CMME algorithm is evaluated on 10 CMaOPs with different features and a variable number of objective functions. Experimental results on three benchmark CMOPs and three real-world applications demonstrate that CMME shows superiority or competitiveness over nine related algorithms.