In orthogonal frequency division multiplexing (OFDM)-based cognitive radio (CR) systems, the optimized algorithms for sub-carrier power allocation face the problems of complex iterative calculation and difficult realization. In this paper, we propose an exponential power distribution function and derive a sub-optimal power allocation algorithm. This algorithm aims to allocate power of in-band subcarriers of cognitive users according to the numerical characteristics of the power distribution function by using a convex optimization numerical method under linear constraints. This algorithm has the advantages of fast calculation speed and easy realization, and reduces the interference to the authorized users, which is caused by the power leakage of the in-band subcarriers of cognitive users to the out-of-band subcarriers. Simulation results show that the proposed algorithm maximizes the inband channel capacity of the cognitive users under certain interference thresholds of the authorized users, thus increasing their transmission rate.