An off-axis three-mirror system with large linear field of view was designed. The system is with a focal length of 1 200 mm, a F-number of 12, a linear field of view of 30°×1°. In the system, x-y polynomial freeform surface was applied as the tertiary mirror surface type to increase the system design degree of freedom, furthermore, in order to bring considerable convenience to alignment, and obtain an axial symmetrical imaging quality about the tangential plane, the x-y polynomial was modified. The design results show that system modulation transfer function value is above 0.45@50 lp/mm, wavefront error maximum value is 0.056λ(λ=0.632 8 μm), RMS wavefront error value is 0.036λ, maximum distortion value is 0.8%, and the imaging quality is symmetrical about the tangential plane. The realizable tolerance values are allocated, and based on Monte Carlo analysis method the tolerance analysis results show that the system RMS wavefront error is less than λ/14. The off-axis three-mirror system has a certain reference value for remote sensor optical system design, and it is suitable for wide swath linear pushbroom imaging system.