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Power control is one of the key technologies in radio resource management, and efficient power control scheme can decrease the interference to other users and save the power consumption. In cognitive radio network, the interference caused by unlicensed user to licensed user is strictly limited. In order to maximize the network utility, a game theoretic approach is proposed. In this paper, a new power control algorithm with a certain type of price coefficient is proposed based on game theory, and it takes the interference to the licensed users into account. Meanwhile, the algorithm also gives attention to both system capacity and fairness index. We can show the existence and uniqueness of the Nash equilibrium of the proposed algorithm further. In addition, its better performance can be indicated by the numeral results.