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Venture capital is a risky and long-term equity investment activity, and venture capitalists widely use the syndication, a jointly investment model, to finance entrepreneurial start-ups. And, the syndication’s successful operation is inseparable from trust between participants. Our paper focuses on trust governance between the leader and the follower, players in the syndication, through constructing an evolutionary game model. In the model, both players adopt Replicator-Dynamics-based learning rules and their strategy space is "Trust, No-Trust". The trust governance mechanism contains two aspects: punishment and reward, both of whose intensity are categorized into three levels, low, middle, and high level. After comprehensively computing and comparing players’ evolutionary stable strategy (ESS), we find relationships between the trust governance mechanism and players’ ESS. If both of the intensities of reward and punishment are at low level, then both the leader and the follower choose “No-Trust”. If both of the intensities of reward and punishment are at high level, then both the leader and the follower choose “Trust”. If the intensity of punishment is at low or middle level, and the intensity of reward is at middle level, then the leader chooses “Trust” and the follower does not. In the intensity of punishment is at middle level, and the intensity of reward is at low or middle level, then the leader chooses “Trust” and the follower does not. If the intensity of punishment is at low level and the intensity of reward is at high level, or if the intensity of punishment is at high level and the intensity of reward is at low level, player’s ESS combination shows a rather varied changes.