A new expected utility (EU) portfolio selection model without short sales is proposed. In the model, the expected utility function is quadratic. The model is solved by the pivoting algorithm. The paper showed in the EU portfolio selection model without the short sales, the relationship between the risk preference coefficient and the expected return is not linear but more complex. The risk preference coefficient could just reflect the investors’ preference in some intervals. We wrote program to calculate the optimal portfolios with the different coefficient. Investors could choose the optimal investment strategy according to both their own risk preference and the expected return of the portfolio.