Imaging of ground multiple moving targets in a synthetic aperture radar (SAR) system is a challenging task due to the fact that targets are defocused owing to motions and contaminated by the strong background clutter. Motivated by recent advances in deep learning, a novel deep convolutional neural network (CNN)-based method, DeepImaging, is proposed for ground moving target imaging (GMTIm). Different from conventional imaging methods relying on the prior knowledge of imaging, the proposed DeepImaging is directly trained to learn an implicit imaging model of multiple moving targets. It is free of motion parameter estimation and iteration process. Then, the trained DeepImaging, as an imaging processor, can be applied to the SAR complex received data after clutter suppression to achieve the multiple moving target imaging and the residual clutter elimination simultaneously. Simulations and experiments on the Gotcha data show that the proposed method achieves significant improvements over existing state-of-the-art GMTIm methods in terms of imaging quality and efficiency.