Metasurfaces that can effectively manipulate electromagnetic waves provide a novel solution to realize efficient terahertz functional devices. However, the chromatic aberration of metasurfaces is a remarkable challenge for their extensive applications. Multi-functional metasurfaces are highly desirable in practical applications. Here, we demonstrate polarization-multiplexing achromatic metasurfaces working in the terahertz regime based on anisotropic meta-atoms which exhibit the formbirefringence. Specifically, a polarization-multiplexing achromatic metalens working in the frequency range from 0.8 THz to 1.2 THz is proposed and verified numerically, which can focus terahertz waves within the working bandwidth to different focal planes by varying the polarization state of an incident terahertz wave; the deviation of focal length is less than 8.88% across the whole working bandwidth. In addition, a polarization-multiplexing achromatic deflector working in the frequency range from 0.8 THz to 1.2 THz is also designed and simulated, which can deflect a terahertz wave within the working bandwidth to different directions by manipulating the polarization state of an incident terahertz wave. The metasurfaces demonstrated here are of great significance for the development of ultra-compact, flexible, and multi-functional terahertz devices based on metasurfaces. © 2022 Optica Publishing Group.