The Brewster effect has been previously reported as an essential mechanism for terahertz (THz) wave sensing application. However, generally in a sensing application, a complex rotation apparatus is required for detecting the slight change in Brewster angle. Here, we propose a graphene-based Brewster angle device operating at a specific terahertz frequency capable of sensing the refractive index at a fixed incident angle. In other words, our sensing device could avoid the impact of Brewster angle shift and eliminate the need for high-precision rotating equipment, which is usually required in traditional sensing applications. The conversion from the refractive index to a Volt-level detectable voltage roots from the tunability of graphene's Fermi level in the external electrical field. A linear correlation between the output voltage and the background refractive index is observed and theocratically analyzed. Furthermore, we present the improvement of our device in terms of sensing range and sensitivity by adjusting the permittivity of the dielectric substrate. As a demonstration of our proposed device, a detection range of 1.1-2.4 and a sensitivity of 20.06 V/RIU for refractive index is achieved on a high-resistance silicon substrate operating at 0.3 THz.