Recently, there has been a significant advancement in image generation technology, known as GAN. It can easily generate realistic fake images, leading to an increased risk of abuse. However, most image detectors suffer from sharp performance drops in unseen domains. The key of fake image detection is to develop a generalized representation to describe the artifacts produced by generation models. In this work, we introduce a novel detection framework, named Learning on Gradients (LGrad), designed for identifying GAN-generated images, with the aim of constructing a generalized detector with cross-model and cross-data. Specifically, a pretrained CNN model is employed as a transformation model to convert images into gradients. Subsequently, we leverage these gradients to present the generalized artifacts, which are fed into the classifier to ascertain the authenticity of the images. In our framework, we turn the data-dependent problem into a transformation-model-dependent problem. To the best of our knowledge, this is the first study to utilize gradients as the representation of artifacts in GAN-generated images. Extensive experiments demonstrate the effectiveness and robustness of gradients as generalized artifact representations. Our detector achieves a new state-of-the-art performance with a remarkable gain of 11.4%. The code is released at https://github.com/chuangchuangtan/LGrad.