The influence of the barrier between metal electrodes and graphene on the electrical properties was studied on a two-electrode device. A classical barrier model was used to analyze the current-voltage characteristics. Primary parameters including barrier height and effective resistance were achieved. The electron transport properties under magnetic field were further investigated. An abnormal peak-valley-peak shape of voltage-magnetoresistance curve was observed. The underlying mechanisms were discussed under the consideration of the important influence of the contact barrier. Our results indicate electrical properties of graphene based devices are sensitive to the contact interface.