The multi-period portfolio optimization models were introduced to overcome the weaknesses of the single-period models via considering a dynamic optimization system. However, due to the nonlinear nature of the problem and rapid growth of the size complexity with increasing the number of periods and scenarios, this study is devoted to developing a novel league championship algorithm (LCA) to maximize the portfolio’s mean-variance function subject to different constraints. A Vector Auto Regression model is also developed to estimate the return on risky assets in different time periods and to simulate different 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 indicate that the quality of portfolios, in terms of the mean-variance measure, obtained by LCA is 10 to 20 percent better than those of the commercial software. This sounds promising that our method can be a suitable tool for solving a variety of portfolio optimization problems.