How to conclude a fair reasonable underwrite price of initial public offering stocks is always a very important issue in the stock market. This article try to quote the adverse selection model to establish an optimal underwrite mechanism. Besides, we investigates the dead weight loss caused from asymmetric information and the affect of social welfare caused by the underwriting contract via the tree-tier (The issuer/ The underwriters/ The retail investors participated in the IPO) hierarchical model of contract theory. Finally, we try to investigate the many phenomena caused by the optimal contract.