The unmanned aerial vehicle (UAV)-borne hyperspectral imaging system has the advantages of high spatial resolution, flexible operation, under-cloud flying, and easy cooperation with ground synchronous tests. Because this platform often flies under clouds, variations in solar illumination lead to irradiance inconsistency between different rows of hyperspectral images (HSIs). This inconsistency causes errors in radiation correction. In addition, due to the accuracy limitations of the GPS/inertial measurement unit (IMU) and irregular changes in flight platform speed and attitude, HSIs have deformation and drift, which is harmful to the geometric correction and stitching accuracy between flight strips. Consequently, radiation and geometric error limit further applications of large-scale hyperspectral data. To address the above problems, we proposed an integrated solution to acquire and correct UAV-borne hyperspectral images that consist of illumination data acquisition, radiance and geometric correction, HSI, multispectral image (MSI) registration, and multi-strip stitching. We presented an improved three-parameter empirical model based on the illumination correction factor, and it showed that the accuracy of radiation correction considering illumination variation improved, especially in some low signal-to-noise ratio (SNR) bands. In addition, the error of large-scale HSI stitching was controlled within one pixel.