In this article, we focus on the problem of relay selection for the cooperative cognitive radio-based Internet of things. In such systems, a pair of primary user devices (PUs) can only communicate with each other through a relay. The relay is selected from a set of multi-slot energy-harvesting (EH)-enabled secondary user devices (SUs). The charging and discharging process of an SD's battery is formulated as a finite state Markov chain, and we can derive the corresponding analytical expression of steady-state distribution. Consider the non-authority of SUs, we analyze the outage performance when SUs are trusted and untrusted. When SUs are trusted, we provide the theoretical analysis expression and the lower bound expression for the outage probability. On the contrary, we propose a destination-assisted jamming strategy to secure primary communication if SUs are untrusted. In addition, we propose a Vickrey auction-based EH-enabled relay selection strategy which can be applied to the secondary system. For this auction strategy, SUs without direct links can transmit signals by selecting an EH-enabled SU as a relay. The winning SU in the process of auction can earn reward. Finally, the simulation results verify that the EH-based transmission can obtain excellent system performance without consuming excess energy, and we also study the effect of different parameters on system outage performance.