The performance of a relay based Half-Duplex (HD) and Full-Duplex (FD) cooperative cognitive radio (CR) network with a RF energy harvesting (EH) is studied in this paper. Co-operative environment includes a network with multiple primary users (PUs), and CRs. The relay node is considered as an EH node which harvests energy (HE) from RF signal (RFS) of source and loop-back interference. The network performance is studied for instantaneous transmission and delay constraint transmission for decode and forward (DF) relaying protocol. The performance is investigated under a relay energy outage constraint and the expression of throughput is redesigned. Expressions of energy outage, data outage and throughput for HD and FD are developed. The impact of several parameters such as transmitting SNR, fractional harvesting time parameter, fractional transmission time parameter, and loop-back interference on the system throughput has been investigated.