In this study, we have separately evaluated the radiative and non-radiative recombination lifetimes for InGaN quantum well (QW) samples with different amounts of ion-implantation damage, and have investigated their temperature dependence. The radiative and non-radiative recombination lifetimes were calculated from photoluminescence (PL) decay time measured by time-resolved PL measurements, combined with the absolute internal quantum efficiency values estimated by the simultaneous photoacoustic and PL measurements. As a result, the experimentally observed radiative recombination lifetimes are almost the same for all samples, while the non-radiative recombination lifetimes are shorter for samples with larger ion-implantation damage. These findings will lead to a comprehensive understanding of carrier dynamics in InGaN-QW optical devices.