We investigated the flux pinning properties in terms of the critical current density (J c) and pinning force density (F p) of MgB2 films with ZnO buffer layers of various thicknesses. At higher thicknesses of the buffer layer, significantly larger J c values are observed in the high-field region, whereas J c values in the low- and intermediate-field regions remain largely unaffected. A secondary point-pinning mechanism other than primary grain boundary pinning is observed in the F p analysis, which depends on the thickness of the ZnO buffer layer. Moreover, a close relationship between the Mg and B bond ordering and the fitting parameter of secondary pinning is obtained, indicating that the local structural distortion of MgB2 induced by ZnO buffer layers with different thicknesses may contribute to flux-pinning enhancement in the high-field region. Discovering further advantages of ZnO as a buffer layer other than the delamination resistance it provides will help to develop a MgB2 superconducting cable with a high J c for power applications.