In this article, we study an orthogonal frequency division multiplexing‐based underlay cognitive two‐way amplify‐and‐forward (AF) relay network. We assume a system model consists of a primary network that has two primary users (PUs) and a secondary network that has two secondary users (SUs) exchanging information in two‐way through a half‐duplex AF relay node. The introduced interference from the secondary network on the primary network should not exceed a maximum allowable level. In our study, we assume a channel model called hybrid channel model. Based on this model, the channels between the PUs and SUs are modeled using free‐space path loss model, while the channels between the SUs are modeled using Nakagami‐m fading model. We analyze the proposed system model in terms of signal‐to‐noise‐ratio (SNR) and outage probability (OP) under three different transmission schemes; two time slots, three time slots, and four time slots schemes. The SNR and OP at one end of the secondary network over the three transmission schemes are mathematically derived. Moreover, Monte Carlo simulation is used to verify derivations. Simulation results coincide well with theoretical results, confirming the correctness of our mathematical derivations. In addition, different scenarios of the system are studied, from which we conclude that different factors, like the transmitted power by the primary transmitter and the positions of primary transmitter and receiver as well as the relay node, have significant effect on the outage performance of the secondary network.