Image de-raining is a hot issue in the low-level tasks of images, in which raindrop removal is critical. Raindrops adhering to glass or camera lenses will significantly reduce the visibility of the scenes. Therefore, removing raindrops will benefit various computer vision tasks, especially outdoor surveillance systems and intelligent driving systems. In this study, we propose a lightweight network (PRSEDNet) to remove raindrops from a single image. With recursive computation, this network uses a convolutional long short-term memory network and a feature extraction module to extract features. In combination with the original image, the final high-quality clear image without raindrops is obtained. The experimental results show that PRSEDNet, compared with the existing deep learning-based raindrop removal algorithms, possesses few parameters and high computational efficiency and can achieve efficient raindrop removal.