In wholesale competition power markets， not only generation companies but distribution companies take part in market competition. The analytic optimal bidding strategy of generation/distribution companies based on the bidding model under wholesale competition power market is deduced. Then co-evolutionary algorithm is used to simulate the operation of the power market and the market equilibrium is achieved. A numerical example is used to illustrate the feasibility of the proposed method and the results indicate that the bidding strategy under market equilibrium is just the optimal one for generation companies and distribution companies.