Considering the interference introduced by primary user, the outage probability of cognitive relay networks under imperfect channel state information is analyzed based, on the relay selection for the maximum channel gain. In addition, the mathematical optimization model of maximizing the spectrum efficiency under the interference constraint of primary user and the QoS requirement of cognitive user is proposed for cognitive relay networks. Then, the optimal solution of the model is obtained with the Lagrangian method. The proposed scheme improves the spectrum efficiency of cognitive relay networks on the premise of guaranteeing the transmission performance of primary user. Simulation results show that the proposed power allocation scheme improves the system performance compared with the traditional equal power allocation scheme. Meanwhile, it indicates that the approximate spectrum efficiency can be obtained under the perfect channel state and the imperfect channel state. Under the imperfect channel state, the feedback information and the complexity of implementation will be reduced, which is beneficial to the engineering application.