In recent years, deep learning based methods have made significant progress in rain-removing. However, the existing methods usually do not have good generalization ability, which leads to the fact that almost all of existing methods have a satisfied performance on removing a specific type of rain streaks, but may have a relatively poor performance on other types of rain streaks. In this paper, aiming at removing multiple types of rain streaks from single images, we propose a novel deraining framework (GRASPP-GAN), which has better generalization capacity. Specifically, a modified ResNet-18 which extracts the deep features of rainy images and a revised ASPP structure which adapts to the various shapes and sizes of rain streaks are composed together to form the backbone of our deraining network. Taking the more prominent characteristics of rain streaks in the gradient domain into consideration, a gradient loss is introduced to help to supervise our deraining training process, for which, a Sobel convolution layer is built to extract the gradient information flexibly. To further boost the performance, an adversarial learning scheme is employed for the first time to train the proposed network. Extensive experiments on both real-world and synthetic datasets demonstrate that our method outperforms the state-of-the-art deraining methods quantitatively and qualitatively. In addition, without any modifications, our proposed framework also achieves good visual performance on dehazing.