We experimentally and theoretically investigated the mode competition and output power characteristics in the terahertz quantum cascade lasers of first-order distributed feedback based on a buried grating. The simulations obtained the relationships of the etching depth of a buried grating with the waveguide loss, optical confinement factor, radiation loss, and radiation efficiency of two band-edge modes. Theoretical calculations have obtained the relationship between buried grating corrosion depth and waveguide loss, optical confinement factor, radiation loss, and radiation efficiency of the two band-edge modes. Theoretical calculations show that the distributed feedback structure of the buried grating can adjust the threshold gain and radiation efficiency of the laser while ensuring the stable single-mode operation of the laser in the high-band side mode by changing the corrosion depth. Experimental and test results show that the laser radiation wavelength is proportional to the period of the buried grating and the laser could operate stably in a single mode in the whole dynamic range. The single-mode laser can cover the range from 86.2 μm to 91.7 μm, the side mode rejection ratio can reach 25 dB, and the maximum output power is 9.1 mW. This work is helpful for the development of high-performance single-mode terahertz lasers and phase-locked laser arrays.