A broadband switchable bifunction terahertz polarization converter based on a Dirac semimetal is proposed in this paper. The polarization converter comprises a resonant structure and a gold film separated by a polyethylene cyclic olefin copolymer dielectric layer. By adjusting the Fermi energy level of the Dirac semimetal, the designed metasurface can be switched from a quarter-wave plate to a half-wave plate. The numerical simulation results revealed that when the Fermi energy level is 70 meV, the metasurface is a quarter-wave plate, which can convert the incident linearly polarized wave into a left-handed circularly polarized wave at frequency ranging from 1.955-2.071 THz. The plate converts the linearly polarized wave into a right-handed circularly polarized wave at frequency ranging from 2.606-3.490 THz. Furthermore, the ellipticity associated with frequency ranging from 1.955-2.071 THz and 2.606-3.490 THz is close to ±1. The metasurface behaves as a half-wave plate capable of converting y-polarized waves into x-polarized waves at frequency ranging from 2.599-3.638 THz. The corresponding polarization conversion rate exceeds 90% when the Fermi energy level is 160 meV. In addition, compared with other structures, the structure can maintain the same performance at a large incident angle, and its polarization switching performance can be dynamically tuned by changing the Fermi energy level of the Dirac semimetal. The design method can be employed in various fields including wireless communication, terahertz sensing, and imaging.