In cognitive radio network, power control is necessary to not only decrease the interference among the unlicensed users, but also avoid the negative effect to the licensed users. In this paper, a noncooperative power control model is proposed for the unlicensed users using game theory. In order to restrict the interference to the licensed users, an exponential part indicating the effect to the licensed users is added into the pricing function. Through game theoretic deduction, it is obtained that a unique Nash equilibrium solution exists under appropriating parameter value of the payoff function. Further, the Nash equilibrium solution of the proposed power control game with exponential pricing is Pareto optimality and achieves maximum total throughput under strict constraint of the interference temperature limitation. The appropriate value of the new parameter in the pricing function is discussed. The performance of the proposed power control algorithm is investigated by numeral results.