Airborne hyperspectral remote sensing is an important application in the ecological monitoring of the environment in mining areas, and accurate preprocessing of the original images is the key to quantitative information retrieval. The original image data need radiation correction to acquire surface reflectance data. Due to the impact of the field angle, incidental radiance, and the bidirectional reflectance distribution function (BRDF), there can be a brightness gradient between adjacent strips, which leads to radiance difference and obvious chromatic aberration of the mosaicked images. We propose a novel data correction method for seamless mosaicking of airborne hyperspectral images. Firstly, visible and near-infrared (VNIR) and shortwave infrared (SWIR) sensors are calibrated in the laboratory, and the radiation calibration model of the sensor is established by an integrating-sphere system. A correction function is then established by combining the BRDF effect and the radiation attenuation coefficients. We also normalize the exposure time, sun altitude angle, and sensor altitude angle according to the flight strip. The results showed that this method is able to eliminate the signal distortion, allowing the seamless mosaicking of 37 strip images which were taken in different date and conditions in the study area. After the atmospheric correction of the imagery was completed, the accuracy of the preprocessing results was evaluated by field-measured ASD spectroradiometer data. The coefficient of determination R² of the results for the reflectance was greater than 0.9. The experiments show that the proposed method has a good performance in radiation accuracy, and can provide high-quality hyperspectral data for the follow-up application of the ecological monitoring of a mining area.