The process of CEO incentive and supervision, in which the special committee plays an important role, has always been a hard problem to solve in modern corporate governance. Considering the conflicts of interest between the compensation committee, audit committee, and the CEO, this paper constructed a game model of incentive and supervision within the board of directors and analysed the strategic choices of all three and the influencing mechanisms in different contexts. The results show that there is no totally stable strategy point in the system and that there are different strategy choices in different situations; the CEO’s strategy choice is influenced by both the compensation committee and the audit committee, the incentive strategy of the compensation committee will promote the CEO’s self-interested behaviour, and the supervision strategy of the audit committee is inhibitive. The function of the special committee is dependent on its initial intention and the intensity of action. In the situation of excessive incentive by the compensation committee, the strategy choice of audit committee has periodicity, and the CEO and audit committee have periodic discretionary choice game. This study provides insight into the internal governance of the board of directors, particularly special committees, which create the incentive and supervisory contracts.