With the increasing requirement of space information acquisition ability, the dynamic high-resolution remote sensing has become a new hotspot research in space optical fields. The field-bias coaxial three-mirror optical system has the advantage of long focal length, small volume, high level of lightweight and high quality image, which can satisfy the high-resolution, multi-spectrum, versatility and low cost requirement for the LEO video satellite, so it is widely used in the field of the dynamic high-resolution space sensing field. Based on the Gaussian optics and three-mirror aberration theory, the common aperture optical system with area array imaging in visible spectrum and linear push-broom imaging in NIR and MIR spectrum was designed. The focal length for visible spectrum is 4.1 m, the focal length for NIR spectrum is 2.6 m and the focal length for MIR spectrum is 1.85 m, the aperture of three systems is 520 mm, field of view is 0.6°×0.6°. The optical structure is convenient for area array imaging, and the imaging quality of the optical system approaches the diffraction limit. The total length of the optical system is less than f′visible/3.7, and is easily implemented because of the relatively loose tolerance about processing and assembling.