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 $4.35298 pm 0.00004$ days. The transit has a depth of 9 mmag, 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 $R_p sim 1.06 - 1.21 R_J$ 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$_{*} = 1.03^{+0.11}_ {- 0.09} M_{odot}$) and metallicity ([M/H]=$0.0pm0.2$), but is possibly older ($8.5^{+ 5.5}_{- 4.9}$ Gyr).