In this paper, a metamaterial structure with a double-layer split square ring and a double C-shaped structure is designed, which has dual-band electromagnetically induced transparency effects in the terahertz band. This structure has transmission peaks at 1.438 THz and 1.699 THz. Through the analysis of the surface current distribution, the reasons for the dual-band electromagnetically induced transparency are discussed. The effect of the designed metamaterial on the transmission window is studied when the opening size of the open square ring and the distance of the double C-shaped structure and the incident angle are changed. At an incident angle, the transmission spectrum of the designed material changes greatly, implying that it is highly sensitive to angle. The research results show that the structure has potential applications in sensors and angle filters.