The terahertz quantum cascade laser (THz QCL) has a wide gain spectrum, and the emission is often multiple-longitudinal mode when using the conventional Fabry-Perot cavity. A second-order distributed feedback THz QCL can eliminate the mode degeneracy to realize the single longitudinal mode lasing by means of surface radiation loss. Based on the coupled-mode theory, the computational formulas of the basic parameters for the second-order distributed feedback THz QCL with the single-side metal waveguide are deduced. The influences of the grating structure parameters on the coupling coefficients, threshold gain, photon density, and external differential quantum efficiency is investigated. When the grating with a duty cycle of about 0.15 and a depth in the active region of 0.5 μm is etched on the waveguide with a natural cleavage plane, the threshold gain is low, the photon density distribution within the cavity is uniform, and the single longitudinal mode emission can be achieved.