We have designed a near-infrared wavelength Si/CaF₂ DFB quantum cascade laser and investigated the possibility of single-mode laser oscillation by analysis of the propagation mode, gain, scattering time of Si quantum well, and threshold current density. As the waveguide and resonator, a slab-type waveguide structure with a Si/CaF₂ active layer sandwiched by SiO₂ on a Si (111) substrate and a grating structure in an n-Si conducting layer were assumed. From the results of optical propagation mode analysis, by assuming a λ/4-shifted bragg waveguide structure, it was found that the single vertical and horizontal TM mode propagation is possible at the designed wavelength of 1.70µm. In addition, a design of the active layer is proposed and its current injection capability is roughly estimated to be 25.1kA/cm², which is larger than required threshold current density of 1.4kA/cm² calculated by combining analysis results of the scattering time, population inversion, gain of quantum cascade lasers, and coupling theory of a Bragg waveguide. The results strongly indicate the possibility of single-mode laser oscillation.