The Multi-Period Portfolio Optimization (MPPO) models have been introduced to overcome the weaknesses of the single-period models via considering a dynamic optimization system. However, considering the nonlinear nature of the problem and rapid growth of the size complexity with increase in the number of periods and scenarios, this study is devoted to developing a novel League Championship Algorithm (LCA) to maximize the mean variance function of the portfolio subject to di erent constraints. A Vector Auto-Regression (VAR) model was developed to estimate the return on risky assets in di erent time periods and to simulate di erent scenarios of the rate of return, accordingly. Besides, we proved a valid upper bound of the objective function based on the idea of using surrogate relaxation of constraints. Our computational results based on sample data collected from S&P 500 and 10-year T. bond indices indicated that the quality of portfolios, in terms of the mean variance measure, obtained by LCA was 10 to 20 percent better than that by the commercial software. It seems promising that our method can be a suitable tool for solving a variety of portfolio optimization problems.