Solving multi-objective optimization problem using evolutionary algorithm has attracted much attentions and the great progresses have been made in the past decades. The whole history of the research on multi-objective evolutionary algorithm (MOEA) is divided into three periods. After the features of the researches of MOEA and the research achievements are briefly reviewed, the new progresses of MOEA are described in detail since 2003. The various strategies such as co-evolution, parallel implementation and the dynamic evolution have been introduced into MOEA. Finally, the prospects of MOEA in the future are discussed.