A selection method for the sub-band stitching optical glass combination is proposed. The apochromatic equation is solved by the least square method, and the optimal glass combination which can effectively correct the tertiary spectrum is obtained. A broadband long-focus optical system is designed based on this optical glass combination with a wavelength range of 0.45-1.014 μm, a focal length of 400 mm, an F number of 6, and a full field of view of 10°. This system consists of three kinds of optical glasses and seven spherical lenses, and the modulation transfer function (MTF) of this system is closed to the diffraction limit. The research results show that the calibration of the tertiary-spectral residuals in the apochromatic optical system can be achieved with this proposed method.