A tunable demultiplexer with three output channels infiltrated by liquid crystal (LC) is presented, which is based on a metal-insulator-metal (MIM) waveguide. The operating frequencies of the three output channels can be tuned simultaneously at will by changing the external bias electric field applied to the LC. By analyzing the Fabry-Pé / rot (FP) resonance modes of the finite-length MIM waveguide both theoretically and numerically, the locations of the three channels are delicately determined to achieve the best demultiplexing effects. Terahertz (THz) signals input from the main channel can be demultiplexed by channels 1, 2 and 3 at 0.7135 THz, 1.068 THz and 1.429 THz, respectively. By applying an external electric field to alter the tilt angle of the infiltrating LC material, the operating frequencies of channels 1, 2 and 3 can be relatively shifted up to 12.3%, 9.6% and 9.7%, respectively. The designed demultiplexer can not only provide a flexible means to demultiplex signals but also tune operating bands of output channels at the same time.