Many-objective (four or more objectives) optimization problems pose a great challenge to the classical Pareto-dominance based multi-objective evolutionary algorithms (MOEAs), such as NSGA-II and SPEA2. This is mainly due to the fact that the selection pressure based on Pareto-dominance degrades severely with the number of objectives increasing. Very recently, a reference-point based NSGA-II, referred as NSGA-III, is suggested to deal with many-objective problems, where the maintenance of diversity among population members is aided by supplying and adaptively updating a number of well-spread reference points. However, NSGA-III still relies on Pareto-dominance to push the population towards Pareto front (PF), leaving room for the improvement of its convergence ability. In this paper, an improved NSGA-III procedure, called θ-NSGA-III, is proposed, aiming to better tradeoff the convergence and diversity in many-objective optimization. In θ-NSGA-III, the non-dominated sorting scheme based on the proposed θ-dominance is employed to rank solutions in the environmental selection phase, which ensures both convergence and diversity. Computational experiments have shown that θ-NSGA-III is significantly better than the original NSGA-III and MOEA/D on most instances no matter in convergence and overall performance.