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Resource allocation is one of the key issues to improve the efficiency of spectrum utilization in cognitive radio networks. It has been widely investigated with the assumption that the secondary users have a good knowledge of the channel state information of primary system. However, it is not reasonable in practice owing to the imperfect sensing. In this paper, a high-efficiency resource allocation scheme is proposed by considering the imperfect spectrum sensing. Particularly, in order to solve the problem of interference and lower efficiency of spectrum utilization, interference constraints and quality of service requirement are considered to reduce the impact from imperfect spectrum sensing. The goal of the presented scheme is to maximizing the capacity under the interference constraints of primary users. Simulation results indicate that the proposed resource allocation scheme can represent the better performance successfully.