High energy-efficient wireless communication has become hot due to global low-carbon economy. The systems total transmitting power can be saved by resource allocation in cooperative spectrum sharing networks. In cooperative spectrum sharing, the secondary user relays the primary users traffic, as a return, the secondary user is admitted to access the licensed spectrum for its own data transmission. An optimal power and time allocation are presented to minimize the overall energy consumption with the users service quality guaranteed in cooperative spectrum sharing. We formulated it as a convex problem and achieve its optimal power and time allocation in closed form. We analyze the performance of two different transmission protocols for the single relay channel.