The Environmental/Economic Dispatch EED puzzle of power system is actually a classic constrained multi-objective optimization problem in evolutionary optimization category. However, most of its properties have not been researched by its aboriginal Pateto Front. In a meanwhile, the multi-objective evolutionary algorithm based on decomposition(MOEA/D) is a well-known new rising yet powerful method in multi-objective evolutionary optimization domain, but how to run it under constrained conditions has not been testified sufficiently because it is not easy to embed traditional skills to process constraints in such special frame as MOEA/D. Different from non-dominated sorting relationship as well as simply aggregation, this paper proposes a new multi-objective evolutionary approach motivated by decomposition idea and some equality constrained optimization approaches to handle EED problem. The standard IEEE 30 bus six-generator test system is adopted to test the performance of the new algorithm with several simple parameter setting. Experimental results have shown the new method surpasses or performs similarly to many state-of-the-art multi-objective evolutionary algorithms. The high-quality experimental results have validated the efficiency and applicability of the proposed approach. It has good reason to believe that the new algorithm has a promising space over the real-world multi-objective optimization problems.