This paper focuses on the bi-level optimization problem of biddings and clearing of power suppliers under the coupling of electricity, carbon, and green certificate market. Firstly, a bi-level optimization decision model of multi-entities under the coupling of electricity market, carbon market and green certificate market is formulated, in which the constraints of DC power flow, the piecewise linear bidding method and the inverse-demand linear relationship between volume and price of green certificates are considered. The model can help power suppliers optimize their bidding strategies and improve their ability to benefit from competition. Secondly, a bi-level algorithm based on the optimal value function approximation is proposed to solve the problem. The algorithm constructs the optimal value function of the lower model based on the polynomial basis and least square method, and then converts the bi-level optimization model into a single-level optimization model. Different from the traditional Karush-Kuhn-Tucker method, this method does not introduce new integer variables when simplifying the model, and can achieve fast solution of the model. Finally, simulation analysis verifies the rationality of the proposed model and the effectiveness of the proposed algorithm.