We report the discovery of a transiting planet orbiting the star TYC 2-1155-1. The star, WASP-32, is a moderately bright (V=11.3) solar-type star (Teff=6100 +- 100K, [Fe/H] = -0.13 +- 0.10). The lightcurve of the star obtained with the WASP-South and WASP-North instruments shows periodic transit-like features with a depth of about 1% and a duration of 0.10d every 2.72d. The presence of a transit-like feature in the lightcurve is confirmed using z-band photometry obtained with Faulkes Telescope North. High resolution spectroscopy obtained with the CORALIE spectrograph confirms the presence of a planetary mass companion. From a combined analysis of the spectroscopic and photometric data, assuming that the star is a typical main-sequence star, we estimate that the planet has a mass M_p = 3.60 +- 0.07 M_Jup and a radius R_p = 1.19 +- 0.06R_Jup. WASP-32 is one of a small group of hot Jupiters with masses M_p > 3M_Jup. We find that some stars with hot Jupiter companions and with masses M_* =~ 1.2M_sun, including WASP-32, are depleted in lithium, but that the majority of these stars have similar lithium abundances to field stars.