Abstract: The multi-period mean-variance portfolio selection was presented by taking into account transaction cost, threshold constraints, borrowing constraints and cardinality constraints. Because of the transaction costs, the multi-period portfolio selection is the mix integer dynamic optimization problem with path dependence. The discrete approximate iteration method was designed to obtain the optimal portfolio strategy. Finally, the comparison analysis of the differently desired number of assets in the portfolio selection was provided by a numerical example to illustrate the efficiency of the proposed approaches and the designed algorithm.