The main purposes of this study are to discuss the auditing function of the auditor in the situation that the firm must fund by equity capital under the environment of building and implementing the corporate governance, and to understand the strategy choice of managers and auditors. This study is derived the equilibrium condition and finding by game theory. The research model considers the role of the manager and the auditor. The main results are: Building and implementing the corporate governance will reduce the motivation of collusion between the manager and the auditor, and the manager will report honestly, and the auditor will maintain his independence. The more the effect of auditor's auditing function is, the more the contribution for solving the under-capitalizing problem, and the firm with different investment project must engage the auditor with different professional reputation.