Terahertz technology has attracted wide attention because of its potential applications in diverse fields, such as spectroscopy, imaging, and nondestructive evaluation, but the lack of functional devices, including polarization convertors, is still a major hurdle for these applications. In previous studies on metamaterial-based polarization convertors, only one single polarization conversion is generally achieved. This paper presents a transmissive dual-functional terahertz waveplate based on an all-dielectric metamaterial composed of periodic subwavelength pillars made of pure silicon that can achieve two different polarization conversions (i.e., a combination of quarter- and half-waveplates) at the same operation frequency and for x- and y-polarized incidences, respectively. Theoretical and numerical analyses are provided to illustrate the design principle. A sample is fabricated and characterized, and the experimental results show that the two polarization conversions are obtained at 1.01 THz, which is in good agreement with the corresponding simulations. Such a dual-functional terahertz waveplate will find applications in terahertz systems and the design strategy can be extended to other frequency ranges as well.