We consider the high-dimensional Markowitz optimization problem. A new approach combining regression and estimation of optimal returns is proposed to solve the problem. We prove that under some sparsity assumptions on the underlying optimal portfolio, our solution asymptotically yields the theoretical optimal returns, and in the meanwhile satisfies the risk constraint. To the best of our knowledge, this is the first time that both these goals are achieved. We further conduct simulation and empirical studies to compare our method with some benchmark methods, including the equally weighted portfolio, the bootstrap-corrected estimator by Bai, Liu and Wong (2009) and the covariance-shrinkage method by Ledoit and Wolf (2003). The results demonstrate substantial advantage of our method, which attains high level of returns while keeping the risk well controlled by the given constraint. Based on joint work with Mengmeng Ao and Yingying Li.