The optimization of the network throughput and transmission range is one of the most important issues in cognitive relay networks (CRNs). Existing research has focused on the dual-hop network, which cannot be extended to a triple-hop network due to its shortcomings, including the limited transmission range and one-way communication. In this paper, a novel, triple-hop relay scheme is proposed to implement time-division duplex (TDD) transmission among secondary users (SUs) in a three-phase transmission. Moreover, a superposition coding (SC) method is adopted for handling two-receiver cases in triple-hop networks with a cognitive relay. We studied a joint optimization of time and power allocation in all three phases, which is formulated as a nonlinear and concave problem. Both analytical and numerical results show that the proposed scheme is able to improve the throughput of SUs, and enlarge the transmission range of primary users (PUs) without increasing the number of hops.