The single-photon source in mid-infrared (MIR) band is very important for the next generation of quantum sensing, quantum communication and quantum imaging. At present, the commonly used method of generating MIR single-photon source is based on the spontaneous parametric down conversion (SPDC) process in the periodically poled lithium niobate (PPLN) crystal. However, the spectral purity of single-photon source based on the ordinary PPLN is not high, specifically, its maximum value is only about 0.82, which affects the fidelity of quantum information processing scheme. In this paper, 4000 polarized domains in a 30-mm-long LN crystal are customized by using the domain design theory. The sidelobes in the phase matching function are eliminated, and the Gaussian distribution is obtained. The calculated spectral purity of the single-photon source can reach 0.99, and its tunable range is 2.7–3.3 μm. The customized poled lithium niobate (CPLN) is expected to provide a single-photon source with excellent performance for the study of quantum information in the MIR band.