Abstract: The spectrum resource is becoming more and more scarce with the increased variety of the wireless communications, while, on the other hand, the current licensed and fixed spectrum allocation strategy often brings low utilization of spectral resource or even unused. Right aimed on this issue that Cognitive Radio has emerged as a hot topic in wireless communication in recent years. The basic idea of Cognitive Radio is that cognitive users have the ability to determine which portions of the spectrum is available and then dynamically alter its power, frequency, modulation, coding and other parameters to efficiently utilize vacant spectrum without harmful interference with other users. The performance of the whole system depends on the effective management of available spectrum resources. So spectrum allocation is one of the most challenging and crucial problems in cognitive radio. In this paper, a joint power and channel allocation algorithm based on fairness is proposed to maximize the normalized system capacity in cognitive radio networks under the constraints of interference temperature for primary (licensed) users and the power level for each secondary (cognitive) user. The poverty line (PL) is introduced to guarantee the number of available channels for each secondary user. We introduce a nonlinear programming model for this problem as well as the solutions, and we also design the associate allocation algorithm and procedure. The performance of normalized capacity cumulative distribution function is compared with different interference threshold (such as -90dBm, -95dBm, -100dBm, -105dBm and -110dBm). The simulation results show that our algorithm performs better with lower interference threshold. That is because the interference is the main constraint of power allocation with lower interference threshold, and our algorithm is right based on interference threshold. Both the system fairness utility and the normalized capacity of the proposed joint power and channel allocation algorithm are significantly improved compared with that of the original version of joint power and channel allocation algorithm without fairness.