Cooperative relaying has been emerging as a key technology in Cognitive radio(CR) networks. A two-way Amplify-and-forward(AF) based multi-relay CR network is considered, where a primary user coexists with a pair of secondary users and multiple relays. A Timeefficient sub-optimal power allocation scheme(TESOPA)based on Cauchy-Schwarz inequality is provided to maximize the total end-to-end transmission rate of the secondary system. TESOPA is proposed under maximal transmission power constraints, while ensuring the quality of service of the primary user during the whole communication process. The computational complexity is sharply decreased by using the Cauchy-Schwarz inequality. Simulation results show that the proposed TESOPA scheme performs very close to the near-optimal Interior point method based power allocation(IPMPA), especially in interference dominant networks where interference constraints play a key role in determining power allocation results instead of maximal transmission power constraints. Cooperative relaying has been emerging as a key technology in Cognitive radio (CR) networks. A two-way Amplify-and-forward (AF) based multi-relay CR network is considered, where a primary user coexists with a pair of secondary users and multiple relays. A Timeefficient sub-optimal power allocation scheme (TESOPA) based on Cauchy-Schwarz inequality is provided to maximize the total end-to-end transmission rate of the secondary system. TESOPA is proposed under maximal transmission power constraints, while ensuring the quality of service of the primary user during the whole communication process. The computational complexity is sharply decreased by using the Cauchy-Schwarz inequality. Simulation results show that that proposed TESOPA scheme performs very close to the near-optimal Interior point method based power allocation ( IPMPA), especially in interference dominant networks where interference constraints play a key role in determining power allocation results instead of maximal transmission power constraints.