In this paper, we propose filter-and-forward beamforming (FF-BF) for cognitive two-way relay networks in which secondary users employ an orthogonal frequency-division multiplexing (OFDM) system. Secondary transceivers communicate with each other through multiple relays to obtain BF gain as well as to suppress the interference between the primary and secondary users who share the same spectrum. We consider two FF-BF design methods to optimize the relay filter. The first method enhances the quality of service of the secondary network by maximizing the worst subcarrier signal-to-interference-plus-noise ratio (SINR) subject to transmit power constraints. The second method suppresses the interference from the secondary network to the primary network through the minimization of the relay transmission power subject to subcarrier SINR constraints. Simulation results show that the proposed FF-BF improves system performance in comparison to amplify-and-forward relay BF.