The nonreflective high-transmittance transmission phenomenon was first discovered for the transverse magnetic wave between two interfaces; this is known as the Brewster effect. However, all high-transmittance phenomena observed so far are subject to a single frequency or angle of incidence. In this study, a terahertz metasurface that can achieve a dual-frequency angle-independent high transmittance is designed and fabricated. The angle-independent high transmittance can be realized depending on the strict match between the longitudinal wave impedance of the metasurface and air. Simulation, theoretical analysis, and experimental results are consistent with each other, proving the design feasibility. The proposed method can be extended to other frequencies; thus, a wide range of applications can be achieved, including ideal filters and spatial phase shifters.