Based on the vector aberration theory, a method to analyze aberration field distribution induced by the Fringe Zernike polynomial off-axis freeform surface is proposed. The analytical expressions of third-order astigmatism and coma of off-axis freeform surface system are deduced. The aberration nodal distribution of off-axis system caused by the freeform surface is analyzed. According to the aberration distribution properties, with proper Zernike terms selected and optimized, an off-axis two-mirror freeform surface long-wave infrared optical system is designed, and the system has an effective focal length of 500 mm and a pupil diameter of 300 mm. The system is compatible with the uncooled infrared detector that has a format of 384 pixel×288 pixel, and the pixel size is 25 μm. The third-order astigmatism and coma nodes of the optimized system are both moved into the field of view, the asymmetric aberration induced by off-axis is balanced, and the imaging quality of the system is close to the diffraction limit that meets application requirements.