Cognitive radio and cooperation communication are two attractive techniques to improve the spectrum utilization.We study the achievable rate of an underlying cognitive two-way relay network.A two-slot two-way relay scheme using successive interference cancellation and network coding techniques is considered to better utilize the insufficient spectrum resource of the cognitive relay network.Optimal power allocation and time division of this scheme are proposed to achieve fairness and maximize the minimum end-to-end transmit rate of bidirectional communications in the network.Numerical results verify the superiority of the proposed scheme over existing schemes in the practical strongly restricted cognitive radio environment.