This paper proposes a multi-period portfolio investment model with class constraints, transaction cost, and indivisible securities. When an investor joins the securities market for the first time, he should decide on portfolio investment based on the practical conditions of securities market. In addition, investors should adjust the portfolio according to market changes, changing or not changing the category of risky securities. Markowitz mean-variance approach is applied to the multi-period portfolio selection problems. Because the sub-models are optimal mixed integer program, whose objective function is not unimodal and feasible set is with a particular structure, traditional optimization method usually fails to find a globally optimal solution. So this paper employs the hybrid genetic algorithm to solve the problem. Investment policies that accord with finance market and are easy to operate for investors are put forward with an illustration of application.