In this work, a broadband terahertz quarter wave plate was designed using high-resistance silicon based on meander-line dielectric metamaterials, which could convert the terahertz linear-polarization incidence to circular-polarization output. The 3D full-wave simulation shows that the birefringence property of the structure can be freely adjusted by properly designing the geometric parameters, which allows to engineer the transmission amplitudes of two orthogonal terahertz linear polarizations to be close to each other(about 0.55), while the phase difference to be 90°. Based on the design, a terahertz quarter wave plate was fabricated using ion-beam etching method, and then experimentally characterized using terahertz time-domain spectroscopy system. The experimental results agree well with the simulations, which indicates that a broadband terahertz quarter wave plate that functions at 1.07-1.41 THz with a high normalized ellipticity over 0.99 was realized, demonstrating the validity of our designing scheme very well. Besides, by changing the geometrical parameters of the structure, two different broadband terahertz quarter wave plates that function at other frequency ranges were further designed, which confirms the tunability of the proposed structure.