In this paper, a transmissive terahertz (THz) quarter wave plate (QWP) has been proposed to realize the linear- to-circular polarization conversion in terahertz range. This quarter wave plate is composed of two dielectric layers and one metallic layer with asymmetric cross slots. In the range of 0.894—1.378 THz, the axis ratio of proposed device is less than 3 dB, and its polarization conversion efficiency is more than 45%. The distributions of surface currents and electromagnetic field density had been proposed to understand the physical mechanism of proposed device. The linear-to-circular polarization conversion can be attributed to the asymmetric transmission along slots. Finally, the simulation results are validated by experiments in terahertz region. The proposed device has simple geometry and good performance, which can be used as a key component in applications of terahertz communications, terahertz imaging and terahertz sensing.