A mid-infrared difference frequency generator (DFG) based on a periodically poled thin-film lithium niobate rib waveguide on a sapphire substrate is theoretically studied. A mode analysis is carried out at the mid-infrared region, and the analysis focuses on the effects of waveguide geometry on effective refractive indices of a few lower-order modes. A complete theory suitable for modeling a DFG based on a waveguide structure is described. Its validity is confirmed by comparing the theoretical results with previously reported experimental data. Explicit expressions are presented for nonlinear conversion efficiency, thermal tunability and quasi-phase matching (QPM) bandwidth. The effects of waveguide geometry and mode hybridization on the effective mode field area and mode overlap factor, which are either inversely or linearly proportional to nonlinear conversion efficiency, are studied in detail. In this article, an optimized mid-infrared DFG with improved geometry that exhibits excellent performance, including a higher nonlinear conversion efficiency of 230–273% W⁻¹cm⁻² in the temperature range of 20–120 °C; a larger temperature tunability of 2.2 nm/°C; a larger QPM bandwidth of ~130 nm; and a higher idler wave output power, as much as −2 dBm when P_p = 20 dBm and P_s = 11.5 dBm, is suggested.