Lithium niobate crystal satisfies the group-velocity-matching condition in 3.2 μm wavelength band, enabling the generation of spectrally uncorrelated biphotons through spontaneous parametric down-conversion (SPDC). However, under this condition, the biphotons typically exhibit an annular distribution in the spatial domain, resulting in reduced photon collection efficiency and diminished source brightness. Therefore, achieving the frequency-uncorrelated and spatial-single-mode states has become an urgent problem that needs to be addressed. In this study, through theoretical calculations and numerical simulations, the spatial distribution of biphotons was optimized.It was found that under specific wavelength and temperature conditions, the two-photons generated in SPDC by periodically polarized lithium niobate and custom polarized lithium niobate can exhibit a beam like distribution in space, with Schmidt number of 1.170 and 1.150. This approach offers a solution for quantum optical experiments in the mid-infrared wavelength range, by providing quantum light sources with frequency-uncorrelated and spatial single-mode characteristics.