Based on the multi-period mean-variance framework, a portfolio selection problem with serially correlated returns of multiple risky assets is studied. Firstly, by using the Lagrange duality principle and the dynamic programming approach, the model is solved explicitly, and closed-form expressions for the efficient investment strategy and mean-variance efficient frontier are obtained. Then, it is further showed that when the market includes a risk-free asset, the efficient frontier is still a straight line in the standard derivation-mean plane. Finally, by utilizing these results, a specific example is provided.