In this paper, a hybrid spectrum access scheme is investigated for a relay based energy harvesting cooperative cognitive radio (CR) network. In the considered network model, a relay harvests energy from RF signal of primary user (PU) as well as from RF signal of CR also. The relay node forwards the CR data to the respective destination and also cooperates in PU transmission as well. The CR follows a hybrid spectrum access scheme, i.e., it employs an underlay scheme of co-existence if PU is found to be present in the given channel else it switches to the overlay scheme of transmission. In overlay scheme, a CR transmits with maximum transmission power while in underlay scheme, it controls its transmission power based on the knowledge of channel state information of the link between CR and PU receiver, to limit the interference at PU receiver. Three new ratio parameters namely, PU–CR time allocation parameter, PU two hop transmission parameter and CR two hop transmission parameter are considered to model the cooperative transmission of PU and CR network where the parameter β takes care of the allocated time for PU and CR transmission and the other two parameters θ and ϕ take care of two hop transmission for PU and CR respectively. Analytical expressions of combined throughput of a CR and PU are developed under the considered network scenario. The performance is investigated in terms of combined throughput of CR, combined throughput of PU, and the overall network throughput for several sensing parameter and new ratio parameters. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.