In view of the difficulty in assessing the risks brought by the uncertainty of grid-connected wind power to the optimal power flow of the power system, a calculation method of overestimate/underestimate confidence risk cost for wind power based on the probability of a wind power opportunity constraint is proposed. Then, a multi-objective optimal power flow model for an environment/economy is established in consideration of wind power confidence risk cost, and a Non-Dominated Sorting Compound Backtracking Search (NSCBS) algorithm is proposed to achieve an efficient and accurate solution for the multi-objective optimal power flow model. Finally, a modified IEEE30-bus test system is taken as an example to calculate the multi-objective optimal power flow considering wind power confidence risk cost. The results verify the effectiveness and superiority of the proposed method. This work is supported by National Natural Science Foundation of China (No. 51867008), Natural Science Foundation of Jiangxi Province (No. 20192ACBL20007) and Science and Technology Project of Jiangxi Province Education Department (No. GJJ1903013).