In communication industry one of the most rapidly growing area is wireless technology and its applications. The efficient access to radio spectrum is a requirement to make this communication feasible for the users that are running multimedia applications and establishing real-time connections on an already overcrowded spectrum. In recent times cognitive radios (CR) are becoming the prime candidates for improved utilization of available spectrum. The unlicensed secondary users share the spectrum with primary licensed user in such manners that the interference at the primary user does not increase from a predefined threshold. In this paper, we propose an algorithm to address the power control problem for CR networks. The proposed solution models the wireless system with a non-cooperative game, in which each player maximize its utility in a competitive environment. The simulation results shows that the proposed algorithm improves the performance of the network in terms of high SINR and low power consumption.