We report the design and performance analysis of an off-axis three-mirror telescope as the fore optics for a new hyperspectral sensor aboard a small unmanned aerial vehicle (UAV), for low-altitude coastal remote sensing. The sensor needs to have at least 4 cm of spatial resolution at an operating altitude of 500 m, 4° field of view (FOV), and a signal to noise ratio (SNR) of 100 at 660 nm. For these performance requirements, the sensor's optical design has an entrance pupil diameter of 70 mm and an F-ratio of 5.0. The fore optics is a three-mirror system, including aspheric primary and secondary mirrors. The optical performance is expected to reach 1/15λ in RMS wavefront error and 0.75 in MTF value at 660 nm. Considering the manufacturing and assembling phase, we determined the alignment compensation due to the tertiary mirror from the sensitivity, and derived the tilt-tolerance range to be 0.17 mrad. The off-axis three-mirror telescope, which has better performance than the fore optics of other hyperspectral sensors and is fitted for a small UAV, will contribute to ocean remote-sensing research.