Driven by abundant satellite imagery, machine learning-based approaches have recently been promoted to generate high-resolution crop cultivation maps to support many agricultural applications. One of the major challenges faced by these approaches is the limited availability of ground truth labels. In the absence of ground truth, existing work usually adopts the "direct transfer strategy" that trains a classifier using historical labels collected from other regions and then applies the trained model to the target region. Unfortunately, the spectral features of crops exhibit inter-region and inter-annual variability due to changes in soil composition, climate conditions, and crop progress, the resultant models perform poorly on new and unseen regions or years. This paper presents the Crop Generative Adversarial Network (CropGAN) to address the above cross-domain issue. Our approach does not need labels from the target domain. Instead, it learns a mapping function to transform the spectral features of the target domain to the source domain (with labels) while preserving their local structure. The classifier trained by the source domain data can be directly applied to the transformed data to produce high-accuracy early crop maps of the target domain. Comprehensive experiments across various regions and years demonstrate the benefits and effectiveness of the proposed approach. Compared with the widely adopted direct transfer strategy, the F1 score after applying the proposed CropGAN is improved by 13.13% - 50.98%