This paper examines the multi-period portfolio optimization problem with transaction costs and fuzzy variables to count for the uncertainty of future returns and liquidities on assets. The portfolio risk is quantified by using the variance of fuzzy returns. Two conflicting optimization objectives, namely, maximizing the terminal wealth and minimizing the cumulative risk of portfolios over the entire investment horizon, are taken into consideration. For solving the proposed model we introduce a new multi-objective evolutionary algorithm. Finally the performance of the proposed algorithm is compared with the NSGAII and MOEA/D with the assistance of real data from FTSE-100 in London.