Abstract: Threshold gain of laser mode in terahertz quantum cascade laser is calculated with finite element method. It shows that contact layer thickness and doping density have far greater impact on threshold gain than waveguide width and lasing wavelength. As thickness and density becoming smaller (greater), threshold gain of TM₁ (TM₀) mode becomes smaller. Far-field characteristics of the beam are analyzed using vector diffraction theory. The beam spot is basically elliptical. With increase of waveguide width or lasing wavelength, far-field divergence angles at x direction decrease or increase linearly. Though the contact layer thickness and doping density for TM₀ mode are different from that for TM₁, their far-field divergence angles at x direction are same. Moreover, far-field divergence angles at y direction are unaffected by waveguide width, and less affected by lasing wavelength. In terms of threshold gain and beam quality, TM₁ is more desirable than TM₀ mode.