In a full-duplex multi-cognitive relay network supported by Simultaneous Wireless Information and Power Transfer （SWIPT）， in order to maximize energy-spectrum efficiency， the relay with the maximum energy harvesting was selected for decoding and forwarding， thus forming an energy-spectrum efficiency trade-off optimization problem. The problem was transformed into a convex optimization problem by variable transformation and concave-convex process optimization method. When the trade-off factor was 0， the optimization problem was equivalent to the optimization problem of maximizing the Spectrum Efficiency （SE）. When the trade-off factor was 1， the optimization problem was equivalent to the problem of minimizing the energy consumed by the system. In order to solve this optimization problem， an improved algorithm that could directly obtain the trade-off factor for maximizing Energy Efficiency （EE） was proposed， which was optimized by combining the source node transmit power and the power split factor. The proposed algorithm was divided into two steps. First， the power split factor was fixed， and the source node transmit power and trade-off factor that made the EE optimal were obtained. Then， the optimal source node transmit power was fixed， and the optimal power split factor was obtained by using the relationship between energy-spectrum efficiency and power split factor. Through simulation experimental results， it is found that the relay network with the maximum energy harvesting is better in EE and SE than the network composed of other relays. Compared with the method of only optimizing the transmit power， the proposed algorithm increases the EE by more than 63%， and increases the SE by more than 30%； its EE and SE are almost the same as the exhaustive method， and the proposed algorithm converges faster.