A detailed study of the electrical transport properties of gate tunable graphene lateral tunnel diodes is presented. The graphene-Al2O3-graphene lateral tunnel diodes are fabricated on Si/SiO2 substrates, and the fabricated devices show rectifying characteristics at the low voltage below 1 V. The rectifying behavior can be controlled by applying back gate voltages. As a result, the devices show high asymmetry and strong nonlinearity current-voltage (I-V) characteristics, which are desirable properties for applications such as optical rectennas and infrared detectors. The electrical transport mechanism of the graphene lateral diodes is analyzed by extracting parameters from the measured I-V characteristics. We find that trap-assisted tunneling from the defect levels in the Al2O3 layer is the most likely mechanism of the forward current of the fabricated graphene lateral diodes.