Abstract: In resource-constrained cognitive radio networks, how to improve the power efficiency of sub-user network is a question worth considering. To address this problem, we first proposed the optimal power allocation algorithm based on the power efficiency of the sub-users in cognitive radio networks. The algorithm not only considers the limit of primary network outage probability on secondary users transmit power , but also the outage probability requirements of secondary network itself at the same time. Second, to further reduce the computational complexity of the nodes, we presents a low complexity suboptimal power allocation algorithm by reducing the dimension of the objective optimization problem, converting it into two sub-problems so as to be solved conveniently. Finally, the simulation shows that compared to optimal algorithm the sub-optimal algorithm brings only limited performance loss, but saves the computing time and storage space effectively; In addition, when the relay node is close to the source node, it is more conducive to improve the power efficiency of the whole system, and the link of source node to the destination than the relay link has a greater impact on system performance.