Cognitive radio (CR) technology is a promising technology that provides opportunistic access to free channels for secondary users (SUs), and enhances the spectrum efficiency. In this paper we present a novel capacity-aware spectrum allocation model for cognitive radio networks. We first modeled interference constraints based on the interference temperature concept and let the SUs to increase their transmission power until the interference temperature on one of their neighbors exceeds its interference temperature threshold. Then, knowing the potential links SINR and bandwidth, we calculated links capacity based on Shannon formula. Next, we modeled the co-channel interference between SUs on each channel using an interference graph. Finally, we formulated a spectrum assignment problem in a form of the binary integer linear problem to find an optimal feasible set of simultaneously active links among all the potential links in an interference graph in a way that overall network capacity would be maximized. To reduce complexity, we also formulated this problem using genetic algorithm (GA) to find a sub optimal solution in less time. Simulation results have shown that our capacity-aware proposed model leads to a considerable improvement in overall network capacity as compared with other solutions. We also showed that maximizing the number of active links between SUs as an objective function does not necessarily maximize network capacity unless we assume that all the potential links are homogeneous in terms of their SINR and capacity, which is not a realistic assumption.