In this paper, a T-type Germanium (Ge) waveguide with the all-normal dispersion profile is designed for mid-infrared supercontinuum (SC) and frequency comb generations. The nonlinearity coefficient of the designed waveguide is calculated as 30.48 W-1·m-1 at the initial pump wavelength of 3.0 μm. Moreover, the group-velocity dispersion is kept low and flat in the considered wavelength range. Simulation results show that with the designed waveguide, the highly coherent and octave-spanning MIR SC can be generated in the wavelength range from 1.85 to 9.98 µm (more than 2.4 octaves) when the pump pulse with wavelength of 3.0 μm, peak power of 900 W, and duration of 120 fs is launched into the 5 mm long waveguide. When the pulse train including 50 pulses at a repetition rate of 100 MHz is used as the pump source, the SC-based frequency comb is obtained.