The Bidirectional Reflectance Distribution Function (BRDF) is a critical spatial distribution parameter in the quantitative research of remote sensing and has a wide range of applications in radiometric correction, elemental inversion, and surface feature estimation. As a new means of BRDF modeling, UAV push-broom hyperspectral imaging is limited by the push-broom imaging method, and the multi-angle information is often difficult to obtain. In addition, the random variation of solar illumination during UAV low-altitude flight makes the irradiance between different push-broom hyperspectral rows and different airstrips inconsistent, which significantly affects the radiometric consistency of BRDF modeling and results in the difficulty of accurately portraying the three-dimensional spatial reflectance distribution in the UAV model. These problems largely impede the application of outdoor BRDF. Based on this, this paper proposes a fast multi-angle information acquisition scheme with a high-accuracy BRDF modeling method considering illumination variations, which mainly involves a lightweight system for BRDF acquisition and three improved BRDF models considering illumination corrections. We adopt multi-rectangular nested flight paths for multi-gray level targets, use multi-mode equipment to acquire spatial illumination changes and multi-angle reflectivity information in real-time, and introduce the illumination correction factor K through data coupling to improve the kernel, Hapke, and RPV models, and, overall, the accuracy of the improved model is increased by 20.83%, 11.11%, and 31.48%, respectively. The results show that our proposed method can acquire multi-angle information quickly and accurately using push-broom hyperspectral imaging, and the improved model eliminates the negative effect of illumination on BRDF modeling. This work is vital for expanding the multi-angle information acquisition pathway and high-efficiency and high-precision outdoor BRDF modeling.