Terahertz modulators with high tunability of both intensity and phase are essential for effective control of electromagnetic properties. Due to the underlying physics behind existing approaches there is still a lack of broadband devices able to achieve deep modulation. Here, we demonstrate the effect of tunable Brewster angle controlled by graphene, and develop a highly-tunable solid-state graphene/quartz modulator based on this mechanism. The Brewster angle of the device can be tuned by varying the conductivity of the graphene through an electrical gate. In this way, we achieve near perfect intensity modulation with spectrally flat modulation depth of 99.3 to 99.9 percent and phase tunability of up to 140 degree in the frequency range from 0.5 to 1.6 THz. Different from using electromagnetic resonance effects (for example, metamaterials), this principle ensures that our device can operate in ultra-broadband. Thus it is an effective principle for terahertz modulation.