An anomalous distortion is often observed in the transfer characteristics of graphene field-effect transistors. We show that the distortion is caused by metal-graphene contacts with no charge-density pinning effect. The pinning effect, where the gate voltage cannot tune the charge density of graphene at the metal electrodes, has been experimentally observed; however, a pinning-free interface is found to be achieved with readily-oxidized metals. While pinning induces a subtle asymmetry to the transfer characteristics, depinning results in a large distortion in the characteristics, which indicates the potent influence of metal-to-graphene carrier doping on the electronic transport properties of graphene.