A terahertz amplitude modulator based on graphene on a metallic square ring resonant structure is proposed. By separating the graphene and the metallic structure with a thin organic dielectric layer, both the resonant frequency and the amplitude of the transmission resonant peak are modulated when graphene is electrically tuned by a bias voltage. A maximal amplitude modulation depth of 72% at the frequency of 0.6 THz is achieved for the fabricated Terahertz modulator. An analysis model based on the transmission line theory is built to explore the modulation mechanism. Results of the transmission spectrum and the amplitude modulation indicate a good agreement between the transmission line theoretical predictions and the experimental measurements.