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Over recent years, power control plays a critical role in the cognitive radio (CR) system. Most of existing works considered power control game under the interference temperature constrains which is a side condition. In this paper, we propose a power control algorithm using game theory. We define a new pricing function which can effectively control the network power consumption. This pricing function has a dynamic coefficient with interference temperature constrains and it is different from user to user. We also prove the existence and uniqueness of Nash Equilibrium (NE) for the above game. Simulation results show that the game with the proposed pricing function can improve the performance of the cognitive user. Furthermore, the new game model guarantees the fairness of cognitive users at a certain extent.