Mid-infrared band 3–5 ${\text{μm}}$ 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band, the traditional methods of generating and amplifying lasers , such as regenerative amplification, are no longer applicable.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 ${\text{μm}}$ . 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 $ {\text{μm}} $ 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 $ {\text{μm}} $ 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.