A terahertz flexible metamaterial quarter-wave plate (QWP) is designed and fabricated using polyimide as the substrate in this paper, with a 3 dB axial ratio bandwidth of 0.51 THz and high polarization conversion efficiency and transmittance. The effect of the incidence angle on the polarization conversion performance of the QWP is discussed by measuring the transmissions at multiple incidence angles. The blocking effect of this QWP combined with a polarizer on the backward reflection of terahertz waves is investigated by terahertz time-domain spectral transmission experiments. By adjusting the angle of the QWP and polarizer with respect to the incident light in the optical path, a blocking efficiency of 20 dB can be achieved at a 20° incidence angle, with a bandwidth of 0.25 THz, a maximum blocking efficiency of 58 dB at 1.73 THz, and an insertion loss of only 1.4 dB. Flexible terahertz metamaterial QWPs and polarizers can effectively block harmful reflected waves in terahertz communication and other systems. They have the advantages of a simple structure, ultra-thinness and flexibility, easy integration, no external magnetic field, and no low-temperature and other environmental requirements, thus having broad application prospects for terahertz on-chip integrated systems.