Based on the analysis of the feature of cognitive radio (CR) networks, we build a relevant interference model. Cognitive users should particularly consider the problem of interference with licensed users and satisfy the signal-to-interference-plus-noise ratio (SINR) requirement at the same time. We propose a new iterative algorithm using the game theory in this paper. We consider not only the SINR requirement as other game algorithms but also the influence of power threshold. The variable power limit is the characteristic of CR. We prove the convergence of the algorithm and the existence of Nash equilibrium. According to different power thresholds, we give an approach for solving the problem of coexistence between licensed user and cognitive user in a cognitive system. The algorithm has the advantage that it can be distributively implemented, and the method converges relatively fast. Numerical results are presented to show that the proposed approach has better antinoise effect and capacity.