Mid-infrared band 3–5 \textμm laser light source has important applications in many fields such as medical treatment, basic science, communication, and industry. Owing to the limitation to available efficient gain media in the mid-infrared band, the traditional methods of generating and amplifying lasers , such as regenerative amplification, are no longer applicable. In order to produce broadband and high-energy mid-infrared laser, in this work we combine quasi-phase matching technology and chirped periodically polarized lithium niobate (CPPLN) crystal for theoretical analysis and numerical design. The second-order nonlinear difference-frequency generation (DFG) process is used to implement the generation of mid-infrared laser via CPPLN. In the differential frequency process, the pump light used is 800 nm in wavelength and the wavelength range of signal light is 0.95–1.6 \textμm. By calculating the dispersion curve of CPPLN crystal, the phase mismatch of difference frequency generation processes with different light signals is obtained. Under the condition of quasi-phase matching, the CPPLN with deliberately poling structures is designed and used to provide phase mismatch compensation in a broad bandwidth. The designed structure can meet the generation of mid infrared laser in a 1.6–5 \textμm band according to the numerical simulations. The conversion efficiencies of mid-infrared laser with different wavelengths at different positions in the crystal are obtained by using nonlinear coupled wave equations and fourth-order Runge-Kutta method. The results show that the mid-infrared laser in a wavelength range of 1.6–5 \textμm can be produced efficiently in a single CPPLN crystal, with an average conversion efficiency of about 15%. The theoretical analysis and numerical simulation for the designed CPPLN crystal can provide good schematic reference and theoretical support for further experimental exploration on generation of mid-infrared laser.