We derived an analytical expression based on the Pao-Sah theory to characterize the electric conduction of ambipolar graphene transistors. We included and solved exactly the contact resistance, thermal excitation of carrier density, quantum capacitance, and the velocity saturation effect. Our model agreed with the experimental results for ion-gel gated graphene transistors. The microscopic conduction behavior was calculated and proved to be helpful for understanding the weak current saturation observed because of the “kink effect.” To achieve a high voltage gain for radio-frequency or analog circuit applications, the carrier velocity should be facilitated to reach saturation before the formation of the minimal carrier point inside the channel, which can be realized by decreasing the channel length and the series contact resistance. Given a finite channel length and the series contact resistance, the optimized gate capacitance can be solved analytically. Considering state-of-the-art device parameters, we find that maintaining a low contact resistance is vital for further improvement of the device performance.