We present an optical design of a space-borne hyperspectral imager (HSI) for Earth observation micro-satellite platforms. Space-borne hyperspectral imaging has many crucial applications in fields such as agriculture, water management, environmental monitoring, mineralogy, and remote sensing. An HSI system capable of ground sampling distance (GSD) less than 15 m with a swath width greater than 15 km, spectral resolution less than 10 nm and operating in Low Earth Orbit (LEO) is designed. The system dimensions are restricted to fit in a volume of less than 0.125 m3. A commercial, cooled HgCdTe type imaging sensor is selected to operate 400-2500 nm of the spectrum for the designed imager. The HSI optical design comprises of an off-axis three mirror anastigmat (TMA) type telescope and a modified-Offner type spectrometer. Modified-Offner type spectrometer design with two Féry prisms as a diffractive element is used. The overall HSI system design meets the performance goals described in this paper work.