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This paper considers the problem of how to construct the optimal multi-period portfolio for investors with loss aversion in fuzzy environment. Firstly, we regard the return rates of the risky assets as fuzzy numbers and use the value function in prospect theory to transform the return rate of a portfolio into perceived value, which can reflect investors' loss aversion. Moreover, due to the fact that investors' perception level toward risk may vary with the loss aversion degree, we propose a new risk measure based on the perceived value. Then, we formulate the objectives of maximizing the cumulative expected perceived value and minimizing the cumulative perceived risk and propose a multi-period portfolio selection model with diversification constraint. Furthermore, to solve the proposed model, we design a multiple particle swarm optimization algorithm with respect to its specific situation. Finally, using the data from real financial market, we construct a real case to illustrate the effectiveness of the model and algorithm. The results show that loss aversion has an important effect on investors' investment decisions, and the proposed model could provide more reasonable strategies for investors with different loss aversion degrees. [ABSTRACT FROM AUTHOR]