We report the discovery of NGTS-4b, a sub-Neptune-sized planet transiting a 13th magnitude K-dwarf in a 1.34d orbit. NGTS-4b has a mass M=20.6+/-3.0M_{Earth}_ and radius R=3.18+/-0.26R_{Earth}_, which places it well within the so-called 'Neptunian Desert'. The mean density of the planet (3.45+/-0.95g/cm^3^) is consistent with a composition of 100 per cent H_2_O or a rocky core with a volatile envelope. NGTS-4b is likely to suffer significant mass loss due to relatively strong EUV/X-ray irradiation. Its survival in the Neptunian desert may be due to an unusually high-core mass, or it may have avoided the most intense X-ray irradiation by migrating after the initial activity of its host star had subsided. With a transit depth of 0.13+/-0.02 per cent, NGTS-4b represents the shallowest transiting system ever discovered from the ground, and is the smallest planet discovered in a wide-field ground-based photometric survey.