Infrared imaging technology is widely used in fields such as medical diagnosis, spectroscopy, and molecular sensing. In recent years, metalens technology has provided a miniaturized and integrated platform for infrared imaging. However, the inherent dispersion of metalenses greatly hinders their application in infrared imaging. The current mainstream method for designing achromatic metalenses involves simulating the metalens and then analyzing relevant performance parameters, which is time-consuming. To address this issue, this study utilizes the field stitching technique, combined with a particle swarm optimization algorithm, to design a full-silicon achromatic metalens with a diameter of 100 μm, operating in the range of 3.7~4.8 μm. The calculated effective focal length of the designed metalens is 219.01 μm, with a coefficient of variation of 1.87% and a maximum focusing efficiency of 49.3%. The designed metalens was simulated and validated using Lumerical FDTD software. A systematic comparison between the simulation results and the stitching results was conducted in terms of the focal length, coefficient of variation, computational time, full width at half maximum, focusing efficiency, and modulation transfer function, confirming the feasibility and accuracy of the field stitching technique. This method can be extended to other wavelength bands and provides a novel approach for designing larger metalenses.