An anomalous distortion is often observed in the transfer characteristics of graphene field-effect transistors. We fabricate graphene transistors with ferromagnetic metal electrodes, which reproducibly display distorted transfer characteristics, and 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 achieved with easily-oxidizable metals. The distortion should be a serious problem for flexible electronic devices with graphene.