Modern finance theories have been increasingly paying attention to nonlinear and asymmetric features of stock returns. In this talk we extend the concept of covariance to generalized covariance by using generalized measure of correlation (GMC). Based on the generalized covariance which is capable of catching the nonlinearity and asymmetry in stock returns, we propose a mean-generalized variance portfolio optimization model by substituting the traditional covariance matrix with the generalized covariance matrix. Further, we design a hybrid algorithm and present the parameter estimation in detail to improve the applicability of our new portfolio optimization model. Finally, out-of-sample empirical studies support that applying our new method can obtain higher return than using the traditional mean-variance model as well as the equal weighting strategy.