The local government's effort in green innovation management directly affects the development of regional innovation. First, considering the dual functions of the central government's incentive and guidance and the local government's task of promoting independent and disruptive innovations, this paper constructs a multi-task principal-agent model between the central and the local governments. Second, this paper studies the relationship between the central government's incentive intensity and the innovation climate coefficient. It clarifies the factors influencing the incentive intensity, innovation climate coefficient, and the local government's effort level. Finally, the central government's incentive strategies are explored using a numerical simulation in the three stages of green innovation management. The results show that: support for local governments from external innovation is limited, and long-term central government incentives must be introduced. By eliminating external uncertainties, reducing the variable cost of innovation promotion, and controlling local governments' risk aversion, the local government can genuinely boost green innovation management. The more accurate the introduction time of the central government's choice of green disruptive innovation incentives, the more conducive it is to the maximization of green innovation management contract revenue. In the green independent innovation promotion stage, the incentive intensity increases as the marginal profit of innovation increases. In the green independent innovation driving green disruptive innovation stage, the incentive intensity of green independent innovation gradually decreases, and that of green disruptive innovation significantly increases. In the green disruptive innovation reconstructing green independent innovation stage, the differentiation between the two incentives is profound, and the process of green innovation is accelerated.