The Terahertz (THz) band antenna configuration operates in the 0.1–10 THz frequency range and offers a stable performance for future 6th Generation (6G) wireless communication systems. However, the available metallic axial mode helix antenna designs exhibit a peak directivity of lower than 18 dBi within 0.5–1 THz, making it inappropriate to be applied in wireless communication systems. Therefore, this study proposed a high-performance THz metallic five-turn axial mode helix antenna with an optimised truncated hollow cone ground plane for 6G wireless communication systems. Following the creation of the proposed antenna design using cost-effective copper (annealed), the truncated hollow cone ground plane of the THz axial mode helix antenna was optimised via simulation in a Computer Simulation Technology Microwave Studio (CST MWS) software and a verification of the proposed THz antenna design in Analysis System High-Frequency Structure Simulator (Ansys HFSS) software for a fair comparison. Based on the results, the proposed THz metallic axial mode helix antenna with optimised truncated hollow cone ground plane recorded an impedance bandwidth of 0.46 THz, Fractional Bandwidth (FBW) of 61.33% for |S11| ≤ -10 dB, and a maximum directivity and realised gain of 21.8 dBi and 21.5 dBi at 0.85 THz, respectively. Within the 0.5–1 THz, the proposed optimised THz antenna design achieved an outstanding performance, including an FBW of more than 50%, excellent directivity of higher than 15.8 dBi, radiation efficiency of greater than 87%, circular polarisation, and low-profile helix turns. In short, the proposed THz metallic axial mode helix antenna with optimised truncated hollow cone ground plane design is appropriate for various THz 6G wireless applications.