Abstract: In order to overcome the limitation of variance in distinguishing income and loss and solve the problem caused by ignoring the fundamentals in MV model, a mixture of Fundamental Indexing and minimum semi-variance portfolio ("FI-semiv"model), taking into consideration 1- and 2-norm transaction costs respectively and aiming to maximize the expected utility of investors, is proposed and solved with the pivoting algorithm. The model is a convex quadratic programming problem with linear equality and inequality constraints. Based on the "rolling sample" approach, the out-of-sample sharp ratios of different models are compared. It turns out that the sharp ratio of the FI-semiv portfolio has been effectively improved, which means that the portfolio is less risky and more efficient.