Metalenses have drawn a lot of interest for use in near-infrared (NIR) bioimaging due to their benefits, such as flexible design, light weight, and simple integration. However, chromatic aberration is inevitable in optical systems, which substantially reduces their imaging quality. A broadband achromatic metalens for linearly polarized light in the range 1200 to 1550 nm is constructed to address this challenge. The phase and dispersion of the incident light are modulated by altering the ratio between the long and short axes of the elliptical nanopillars. Through the application of the particle swarm optimization algorithm, appropriate compensating phases can be added to the phase profiles at various wavelengths to align the real phase with the target phase of the broadband achromatic metalens. The structure of the nanopillar at any position in the metalens can be found from a relative phase library. Our numerical experimental results demonstrate that the proposed metalens has relatively consistent focusing characteristics and robustness in the 1200 to 1550 nm band, with an average focusing efficiency of 83.14%. The proposed high-efficiency robust NIR achromatic metalens can increase the quality of NIR biological imaging and the efficiency of a detector.