When multi-objective optimization problems include several constraints, multi-objective EAs (MOEAs) need to introduce a mechanism to obtain feasible solutions from infeasible ones. In this work we propose a novel constrained MOEA introducing a parents selection based on two-stage non-dominated sorting of solutions and a directed mating in objective space. In the proposed algorithm, first, we classify the entire population into several fronts by non-dominated sorting based on constraint violation values. Then, we re-classify each obtained front by non-dominated sorting based on objective function values, and select the parents population from higher fronts. In this way, superiority of solutions in the same non-dominance level of constraint violation values is determined by non-dominance level of objective function values. It leads to find feasible solutions having better objective function values. In addition, to generate an offspring, after we select a primary parent, we pick solutions dominating the primary parent from entire population including infeasible solutions. Then we select the secondary parent from the picked solutions and apply genetic operators. In this way, we utilize valuable genetic information of infeasible solutions to converge the primary parent towards its search direction in objective space. Through performance verification using SRN, TNK, OSY and m objectives k knapsacks problems, we show that the proposed algorithm achieves higher search performance than the conventional CNSGA-II (Constrained NSGA-II) and RTS algorithms proposed by Ray et al.