There is a race to develop spaceborne high-resolution video cameras since Skysat-1 is launched successfully. To reduce manufacture cost and adapt to small satellite platform, it is urgent to design and develop a long focal length optical system with small volume, light weight, easy implementation and imageable for two-dimensional field of view. The full field of view coaxial three-mirror anastigmat (CTMA) appropriate for two-dimensional field of view imaging is studied. The problems of its inherent secondary obscuration and imaging plane extraction difficulty are solved. The conditions of eliminating the secondary obscuration and the relationship between the total length of the system and the tertiary mirror relay imaging magnification are presented based on paraxial geometry optics. Then the reasonable tertiary mirror relay imaging magnification and other parameters are discussed and obtained. A flat mirror near its exit pupil can be used to deflect the image plane without obscuration. The flat mirror group is used to fold optical path and the total length of the system is decreased. The method and the result for determining the initial structural parameters are presented. The optimized optical system without secondary obscuration is designed, whose effective focal length (EFL), field of view and F number are 10 m, 1.1°×1°, 14.3, respectively. The total length of the system is 1/8 of EFL. Its imaging quality is near diffraction limit.