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Multi-objective energy management of microgrid (MEM-MG) is to optimize the output power of micro-sources to satisfy the practical constraints through the whole optimization process while minimizing the operation costs and air pollutions of the MG system. In this paper, an MEM-MG optimization model is established and the practical constraints are described. Aiming at handling various types of constraints, a dynamic multi-constraints handling strategy (DMCS) is proposed based on multi-objective optimization evolutionary algorithm (MOEA), by which a potential solutions are evaluated from two aspects during the evolutionary process, namely the overall violations and the amount of the violated constraints. The comprehensive evaluation indexes are introduced to estimate the constraints violations of different dimensions as well as the number of the violated constraints. In addition, the common used Deb's constraints handling approach is modified into dynamic evaluation criteria, which can decrease the values of the two factors above simultaneously. Thereafter, DMCS is combined with non-dominated sorting genetic algorithm II (NSGAII) and applied to several MEM-MG optimization problems with different types of constraints. The simulation results are compared with those obtained by other constraints handling approaches. The case studies verify the effectiveness of the proposed DMCS in handling various types of constraints and finding optimal trade-off solutions for MEM-MG optimization problems.