Markowitz (1952, 1959) laid down ground-breaking work on mean-variance upon which the celebrated the Captital Asset Pricing Modcl was derived by Sharpe (1964)and Litner (1964).Yet, no short-sale constrant is imposed, which can lead to unstable allocation when covariance matrix is estimated.Under the framework of Markowitz, the optimal allocation vector that we want can be very different from the estimated optimal allocation vector that we get, due to insintric difficulty of estimating a large covariance matrix.For example, with 2000 stocks, there are already over 2,000,000 elements to be stimatcd and yet the usuable data are usually no more than 2 years.This can result in adverse performance in selected portfolio selected based on empirical data (Fan, Fan and Lv, 2008).We solve this problem by introducing the short-sale constrained mean-variancc portfolio selection.The LARS algorithm (Efron, et al.2004) is proposed to effectively find all solution paths.As the coustraint on short-sale relaxes, the number of selected portfolio varies from 1 to the number of all stocks.This achieves the optimal sparse portfolio selection.Among 2000 stocks, for example, wc are able to identify the optimal m stocks simultaneously for all 1 ≤ m ≤ 2000, their associated allocation vector, and the estimated utility.The conditions under which the selected portfolios using empirical data and the ideal portfolios with known covariance matrix have similar performance are derived.The utility of our new approach is illustrated by simulated examples and empirical studies.