Portfolio selection problems mainly address how to rationally allocate limited funds to different financial assets to balance maximal returns and minimal risks. However, it is difficult for investors to describe the expected return rate and the risk loss rate of securities via crisp numbers due to the big uncertainties in the security market. Interval programming is a powerful tool to deal with these uncertain problems. In this paper, a multi-period portfolio selection model, which takes the expected return rate, risk loss rate of securities and liquidity as objective functions, is first constructed based on interval multi-objective programming. Then, a directional mutation operator is developed to modify the interactive genetic algorithm based on preference polyhedron whose operator mechanism combines with multi-period characteristics of the constructed model to tackle the model. Finally, empirical analysis is conducted on an uncertain interactive evolutionary optimization system. Experimental results demonstrate that the proposed algorithm can find the most satisfied multi-period portfolios corresponding to an investor's different demands.