This paper investigates the power control and resource allocation problem in a simultaneously wireless information and power transfer (SWIPT)-based cognitive two-way relay network, in which two secondary users exchange information through a power splitting (PS) energy harvesting (EH) cognitive relay node underlay in a primary network. To enhance the secondary networks's transmission ability without detriment to the primary network, we formulate an optimization to maximize the minimum transmission rates of the cognitive users by jointly optimizing power allocation at the sources, the time allocation of transmission frames and power splitting at the relay, under the constraint that the transmission power of the cognitive network is set not to exceed the primary user interference threshold to ensure primary work performance. To efficiently solve this problem, a sub-optimal algorithm named the joint power control and resource allocation (JPCRA) scheme is proposed, in which we decouple the non-convex problem into convex problems and use alternative steps in the optimization algorithm to get final solutions. Numerical results reveal that the proposed scheme enhances transmission fairness and outperforms three traditional schemes.