Wireless network-on-chip (WNoC), with associated on-chip antennas, has been recognised as an alternative solution to overcome the performance limitations of wired networks on chip (NoC). Recently, graphene-based WNoC (GWNoC) architecture with graphene patch antennas in terahertz band was proposed as a viable alternative which can outperform traditional WNoC in terms of bandwidth, energy consumption and a number of cores per system. In this study, a novel design of dual-band re-configurable graphene-based square patch antenna is proposed with orthogonal microstrip line structure for WNoC applications. The proposed antenna can act as wireless transceiver at dual bands of 2.15-2.2 and 2.56-2.6 THz. Its performance in terms of directivity, return loss, fractional bandwidth and beam reconfiguration at different chemical potentials has been analysed. © The Institution of Engineering and Technology 2017.