Rapid and accurate access to large-scale, high-resolution crop-type distribution maps is important for agricultural management and sustainable agricultural development. Due to the limitations of remote sensing image quality and data processing capabilities, large-scale crop classification is still challenging. This study aimed to map the distribution of crops in Heilongjiang Province using Google Earth Engine (GEE) and Sentinel-1 and Sentinel-2 images. We obtained Sentinel-1 and Sentinel-2 images from all the covered study areas in the critical period for crop growth in 2018 (May to September), combined monthly composite images of reflectance bands, vegetation indices and polarization bands as input features, and then performed crop classification using a Random Forest (RF) classifier. The results show that the Sentinel-1 and Sentinel-2 monthly composite images combined with the RF classifier can accurately generate the crop distribution map of the study area, and the overall accuracy (OA) reached 89.75%. Through experiments, we also found that the classification performance using time-series images is significantly better than that using single-period images. Compared with the use of traditional bands only (i.e., the visible and near-infrared bands), the addition of shortwave infrared bands can improve the accuracy of crop classification most significantly, followed by the addition of red-edge bands. Adding common vegetation indices and Sentinel-1 data to the crop classification improved the overall classification accuracy and the OA by 0.2 and 0.6%, respectively, compared to using only the Sentinel-2 reflectance bands. The analysis of timeliness revealed that when the July image is available, the increase in the accuracy of crop classification is the highest. When the Sentinel-1 and Sentinel-2 images for May, June, and July are available, an OA greater than 80% can be achieved. The results of this study are applicable to large-scale, high-resolution crop classification and provide key technologies for remote sensing-based crop classification in small-scale agricultural areas.