Due to the relatively weak birefringence of natural materials in terahertz regime, metasurfaces have been proposed for compact terahertz phase modulators since they show effectively strong birefringence only with ultrathin structures. However, previous designs of metasurface show limited phase modulation reaching only up to the quarter-wavelength phase, and there has been no single metasurface design that works for a terahertz half-waveplate. Here, we present a metasurface that modulates the phase variably up to 180 degrees. The phase modulation is achieved by a hyperbolic metasurface composed of periodically arrayed rectangular metal rings with different periods for horizontal and vertical axis. By controlling each period, we show that our hyperbolic metasurface can possess large positive and negative permittivity values for horizontal and vertical axis and the phase shift can reach up to the 180 degrees. To check the validity of our design, we fabricate reconfigurable metasurface films and demonstrate the phase modulation 90 to 180 degrees. All results show good agreement with numerical simulation results.