The unmanned aerial vehicle (UAV) images captured under low-light conditions are often suffering from noise and uneven illumination. To address these issues, we propose a low-light image enhancement algorithm for UAV images, which is inspired by the Retinex theory and guided by a light weighted map. Firstly, we propose a new network for reflectance component processing to suppress the noise in images. Secondly, we construct an illumination enhancement module that uses a light weighted map to guide the enhancement process. Finally, the processed reflectance and illumination components are recombined to obtain the enhancement results. Experimental results show that our method can suppress the noise in images while enhancing image brightness, and prevent over enhancement in bright regions. Code and data are available at https://gitee.com/baixiaotong2/uav-images.git.