This study presents a novel design of a wideband high-gain resonant cavity antenna (RCA) for millimetre and submillimetre wave bands, and its fabrication using additive manufacturing (AM). The proposed RCA antenna consists of a partially reflecting surface and three impedance matching layers fed by a waveguide. AM techniques are utilised to fabricate the design operating at 30 GHz. Two fabrication techniques are assessed for printing the antenna. The first technique is based on printing a dielectric material and fully coating the parts with a metallic layer, while the second technique involves printing the parts in a single process using metal three-dimensional printing. The first technique offers a lightweight solution while the second technique can print the whole model in one run. The antenna design is investigated by both simulations and experiments. The measured results show a 3 dB gain bandwidth of about 10%, and high gain over 15 dBi for all the three resulting antennas. Good agreement between simulation and measurement is obtained. The antenna is of low cost and achieved good performance in terms of wide bandwidth and high gain, thus it is potentially useful for high-speed wireless communications at millimetre-wave and sub-millimetre-wave frequencies.