With the wider and growing number of wireless network users in one side the demand of frequency spectrum of these networks has grown increasingly and the challenge is the lack of frequencies in these networks; in other hand it has resulted in high energy consumption in wireless networks, in order to support the proper service quality. Since wireless network devices use limited energy capacity buffers, they also face the challenge of energy shortages. Cognitive Radio (CR) is an option for confronting the issue of spectrum limitations for future wireless networks. This technology aligns itself with the radio environment. In wireless networks of CR, to enhance the performance of systems, collaboration between two or more devices is required. In this regard, relay technology has been considered for advantages such as diversity, decreasing pathloss and reducing the shadowing effect. also On commonly used half duplex (HD) CRs networks, transmission and reception can’t occur in same time or in same frequency. Full Duplex communication (FD) has capability of sending and receiving in same time and same frequency. The presence of Self Interference (SI) in FD has been a major obstacle to using this method over the last few years for wireless radio networks. Recent research and studies have shown that largely eliminating Self Interference Cancelation (SIC) in FD is possible. To cope with the challenge of energy shortage of battery of wireless nodes, different energy harvesting models have recently been presented. In this research, an FD based relay selection algorithm with energy harvesting capability in cognitive radio network is presented. The secondary user selects a relay between several relays. This selection is based on the channel conditions and energy harvested and stored in the relay buffer. Relay selection is a very important factor in improving the quality of the radio network service. The main objective of this algorithm is to increase the frequency efficiency and energy efficiency at the same time. As the transmit power of both nodes increases, the efficiency of the frequency increases and the energy efficiency decreases, therefore, the optimal sending power for both nodes is calculated. Results after the implementation of the algorithm. The alghoritm of select of FD relay with the energy harvesting capability and its comparison with the HD structure showed that the frequency efficiency in the FD structure is significantly larger than the HD structure, although, if there is no relay selection, the energy efficiency of the HD structure is higher, by selecting the appropriate relay and setting the relay energy buffer capacity The difference in energy efficiency became to very low levels. As a result, the main advantage of FD, that is nearly doubling the frequency efficiency, can be exploited. cognitive radio, FD communication, relay selection, energy harvesting