In order to meet the integrated application requirements of full-spectrum hyperspectral imaging and detection, this paper designs a visible-to-long-wave infrared (LWIR) co-aperture imaging spectrometer. The front image square telecentric objective is realized by an off-axis three-mirror structure, and the spectrum is divided into four segments by the field of view separation and beam splitter. The post spectrometer adopts an Offner structure with asymmetric convex grating, and the magnifications of the middle-wave infrared (MWIR) and LWIR spectrometers are set to 0.90 and 0.61, so as to meet the requirements of design specification and imaging quality. The design and analysis results show that the proposed system achieves a ground coverage width of 30 km at an orbital height of 600 km. The F number of visible spectral band to short-wave infrared (SWIR) spectral band is 2.6, and resolutions of visible/near infrared (VNIR) and SWIR are better than 5 nm and 10 nm, respectively, with a pixel resolution of 30 m. The F number of the MWIR and LWIR spectral bands is 2.3 and 1.5, respectively, and their spectral resolutions are better than 50 nm and 100 nm, with a pixel resolution of 50 m and 74 m. The modulation transfer function (MTF) of each spectral band is close to the diffraction limit at the Nyquist frequency, and the spectral line curvature and color distortion are less than 1/10 of the detector's pixel size.