The metal-graphene contact resistance has been identified to be a key bottleneck for achieving high performance of graphene transistors. It is crucial to understand the electrical properties of graphene and the carrier transport mechanism under the contact metal. Here, we have developed a new method of characterizing the electrical properties of graphene under the metal contact. It was found that the electrical properties of graphene under the metal can be tuned via the back-gate voltage and display ambipolar behavior. A quantum tunneling model for graphene-metal physical contact has been proposed. The probability of electric field-tunable tunneling has been derived from the results of measurements for the first time. The model predicts that even for physical contact the contact resistance can be much lower than 100 Ω μm when graphene is more heavily doped and the interfacial layer is eliminated. This study paves the way to achieving ultralow graphene-metal contact resistance in graphene devices for terahertz applications.