We investigated the influence of surface damage on the critical current density (J(c)) of MgB2 thin films via 140keV Co-ion irradiation. The J(c)(H) of the surface-damaged MgB2 films was remarkably improved in comparison with that of pristine films. The strong enhancement of J(c)(H) caused by a surface damage in MgB2 films can be ascribed to additional point defects along with an atomic lattice displacement introduced through low-energy Co-ion irradiation, which is consistent with the change in the pinning mechanism, from weak collective pinning to strong plastic pinning. The irreversible magnetic field (H-irr) at 5 K for surface-damaged MgB2 films with a thickness of 850 and 1300 nm was increased by a factor of approximately 2 compared with that of a pristine film. These results show that the surface damage produced by low energy ion irradiation can serve as an effective pinning source to improve J(c)(H) in a MgB2 superconductor.