When energy harvesting (EH) technique is applied in Internet of Things (IoT) to replenish energy for low power consumption sensing nodes, e.g., sensors and radio frequency identification (RFID) tags, the end-to-end (e2e) data rate is usually maximized without accounting for the energy consumption at the nodes. In this paper, however, the energy consumption at secondary users (SUs) along a cognitive relaying link is characterized by means of energy efficiency, defined as the achievable data rate per Joule. In particular, the energy states at each node is modelled as a finite-state Markov chain and the transmit power at a node is optimally allocated by jointly accounting for the interference threshold prescribed by primary users (PUs), the maximum allowable transmit power and the harvested energy at the node. To maximize the energy efficiency, a best relay selection criterion is proposed and the subsequent optimal transmit power allocation is initially formulated as a nonlinear fractional programming problem and, then, equivalently transformed into a parametric programming problem and, finally, solved analytically by using the classic Karush-Kuhn-Tucker (KKT) conditions. With extensive Monte-Carlo simulation results, the effectiveness of the proposed relay selection algorithm and corresponding optimal power allocation strategy are corroborated, in terms of the energy efficiency of SUs.