A metamaterial-based terahertz amplitude modulator is proposed with the structure consisting of an open "bow" shaped metamaterial structure, a high electron mobility transistor, an oblique cross feeder and a silicon carbide substrate. Whether the openings of the "bow" shaped metamaterial structure are connected or disconnected will produce different responses to the terahertz waves passing through the structure. The effect of connecting and disconnecting the openings can be simulated by adding high electron mobility transistors to the openings of the "bow" shaped metamaterial structure. When no bias voltage is applied to the gate of the transistor, the opening of the metamaterial structure is equivalent to conduction, and the transmission coefficient to terahertz waves is high; when bias voltage is applied to the gate on the transistor, the opening of the metamaterial structure is equivalent to disconnection, and the transmission coefficient of terahertz waves is low. The simulation results show that the transmission coefficient of the modulator is 0.579 at 0.22THz when no bias is applied to the transistor gate, while it is 0.040 at 0.22THz when bias is applied to the transistor gate. The modulation depth of 93% is obtained by the equation, and the modulator is insensitive to x- and y-polarized incident waves. Meanwhile, the operating principle of this terahertz modulator is studied by analyzing the electric field distribution and surface current distribution at 0.22THz. The terahertz modulator designed in this paper is characterized by high modulation depth, simple structure and easy processing, which has a broad application prospect in the field of terahertz communication.