This study proposes a terahertz branching waveguide directional coupler with a switchable coupling degree. The coupling degree is switched by controlling the conductivity of the vanadium dioxide film on the surface of the first four branches. The simulation results demonstrate that within the frequency range of 180~250 GHz, the coupling degree is (3±0.6) dB. The isolation and return losses exceed 17 dB when the vanadium dioxide conductivity is 2×10⁵ S/m. Similarly, for a vanadium dioxide conductivity of 10 S/m, the coupling degree is (10±0.7) dB. The isolation and return losses are >18 and 20 dB, respectively. The coupler performs exceptionally well under both coupling states, satisfying the design expectations.