Multi-constrained multi-objective optimization is a challenging topic, which is very common in dealing with real-world problems. This paper proposes a novel two-stage ρg / μg framework based on multi-objective evolutionary algorithm (MOEA) to solve the multi-constrained multi-objective optimization problems (MCMOPs), which dynamically balances the diversity and convergence of solutions. During the multi-constraints handling process, ρg / μg -MOEA makes the reduction of violated constraints as its primary goal, and converges to feasible regions by a proposed ρg -criterion based constraints relaxation method. Moreover, in the late stage of evolution, by introducing the improved dynamic stochastic ranking (DSR) strategy, the “potential” infeasible individuals are utilized to find more feasible regions, which would guarantee a good distribution of the obtained Pareto frontiers. Thereafter, the proposed framework combined with non-dominated sorting genetic algorithm II (NSGAII) is applied to ten benchmark functions and a series of real-world MCMOPs, and the performances are compared with those obtained by some state-of-the-art constraints handling methods. Experimental results indicate that the proposed ρg / μg framework outperforms the current efficient methods in dealing with test CMOPs, and can achieve satisfactory results when solving real-world MCMOPs.