We report on the discovery of WASP-37b, a transiting hot Jupiter orbiting a mv = 12.7 G2-type dwarf, with a period of 3.577471 pm 0.00001 d, transit epoch T0 = 2455338.6188 pm 0.0006 (HJD), and a transit duration 0.1304 pm 0.0018 d. The planetary companion has a mass Mp = 1.80 pm 0.17 MJ and radius Rp = 1.16 pm 0.07 RJ, yielding a mean density of 1.15 pm 0.15 times that of Jupiter. From a spectral analysis and comparisons with stellar models, we find the host star has M* = 0.925 pm 0.120 Msun, R* = 1.003 pm 0.053 Rsun, Teff = 5800 pm 150 K and [Fe/H] = -0.40 pm 0.12. WASP-37 is therefore one of the lowest metallicity stars to host a transiting planet.