The influence of chromatic aberration in a spectral imaging system leads to spectral overlap of an image. This study combines single-pixel imaging and computational ghost imaging in a spectral imaging system， with an achromatic lens of 900-1 700 nm focal length to correct for chromatic aberration. First， the chromatic aberration of achromatic lenses made of different materials was calculated， and a suitable lens was selected accordingly； its aberration-correction was improved by an order of magnitude compared with other lenses. Second， the effects of chromatic aberration on spectral imaging systems and the differences between single-pixel imaging and computational ghost imaging were analyzed. Finally， two spectral imaging systems were compared through simulation and experimental analysis. The experimental results indicate that in the 900-1 700 nm wavelength range， the single-pixel spectral imaging system based on an achromatic lens achieves better image reconstruction results， with peak signal-to-noise ratio （PSNR） ］and structural similarity （SSIM） improvements of 3.93 dB and 0.96%， respectively. Simulations and experiments verify that the near-infrared single-pixel spectral imaging system based on an achromatic lens performs better than computational ghost spectral imaging.