Mid-infrared quantum light sources hold broad application prospects in fields such as gas sensing and infrared thermal imaging. However, currently used mid-infrared quantum entangled light sources primarily rely on bulk periodically poled lithium niobate (PPLN) crystals, which limits brightness and integration. This paper proposes a theoretical scheme based on lithium niobate thin films, in which 1556.9 nm pumping is used to generate entangled photon pairs with a central wavelength of 3113.8 nm. By optimizing the waveguide structure and periodic polarization design, type-II phase matching and group velocity matching are achieved. This enables transverse electric (TE)-polarized pump input to be down converted to generate photon pairs with TE and transverse magnetic (TM) polarizations. Furthermore, by combining a domain arrangement algorithm used for the customized design of polarization direction in PPLN waveguides, precise phase matching is achieved, resulting in a quantum light source with a purity as high as 0.999 and a brightness of 6.18×10⁶ cps/mW, which is three orders of magnitude higher than that of the bulk PPLN crystal source. This study provides a promising solution for realizing high-brightness, high-purity on-chip quantum light sources in the mid-infrared band.