With the development of unmanned airborne vehicle (UAV) remote sensing technology, miniature high-resolution imaging spectrometers are greatly needed. In order to improve remote sensing efficiency and get wider coverage, it’s urgent to design and develop fore-optics with wide field of view and waveband for imaging spectrometer. As the refractive system has no central obscuration and it’s conducive to manufacture and assemble, so it’s used for our fore-optics. The key is the correction of secondary spectrum of systems working in broad waveband and meeting the requirement of imagery telecentricity to be appropriate for linear pushbroom imaging system. Suitable glasses are selected on the Glass Map, from where each glass has an Abbe number υd and Partial Dispersion. Based on the theory of Gaussian Optics and Seidel third-order aberration theory, the paper derives apochromatic formula, and the power of individual lenses can be calculated. Then with a required value of spherical aberration and coma, this paper derives equations to calculate the initial structure of apochromatic optical systems. Finally, optimized refractive SWIR fore-optics working in 1μm-2.5μm with effective focal length (EFFL) of 11mm is reported. Its full field and F-number are respectively 40°, F/2.8. The system has many advantages such as simple and compact structure, small size, near diffraction-limited imaging quality, small secondary spectrum and imagery telecentricity. Especially it consists of spherical surfaces that can greatly reduce the difficulty and the cost of manufacture as well as test, which is applicable for SWIR imaging spectrometer with wide field of view.