We report the discovery of WASP-13b, a low-mass M_p_=0.46^+0.06^_-0.05_ M_J_ transiting exoplanet with an orbital period of 4.35298+/-0.00004days. The transit has a depth of 9mmag, and although our follow-up photometry does not allow us to constrain the impact parameter well (0<b<0.46), with radius in the range R_p_~1.06-1.21R_J_ the location of WASP-13b in the mass-radius plane is nevertheless consistent with H/He-dominated, irradiated, low core mass and core-free theoretical models. The G1V host star is similar to the Sun in mass M_*_=1.03^+0.11^_-0.09_M_{sun}_ and metallicity ([M/H]=0.0+/-0.2, but is possibly older (8.5^+5.5^_-4.9_Gyr).