In recent years, multi-objective optimization problems (MOPs) have attracted more and more attention, and various approaches have been developed to solve them. This paper proposes a new multi-objective evolutionary algorithm (MOEA), namely Pareto partial dominance on two selected objectives MOEA (PPDSO-MOEA), which calculates dominance between solutions using only two selected objectives when choosing parent population. In the proposed algorithm, two objectives are mainly selected with the first and the second largest distances to the corresponding dimension of the best point. PPDSO-MOEA switches the two-objective combination in every I-g generation to optimize all of the objective functions. The search performance of the proposed method is verified on many-objective 0/1 knapsack problems. State-of-the-art algorithms including PPD-MOEA, MOEA/D, UMOEA/D, and an algorithm selecting objectives with random method (RSO) are considered as rival algorithms. The experimental results show that PPDSO-MOEA outperforms all the four algorithms on most scenarios.