Local climate zones (LCZ) describe urban surface structures, supporting studies of urban heat islands, sustainable urbanization, and energy balance. The existing studies mapped LCZs from satellite images using scene-based classification, which trained deep-learning classifiers by labeled image patches, segmented satellite images into patches by sliding windows to match the size of training data, and finally classified the segmented patches to obtain LCZ maps. However, sliding windows are different from the real footprints of LCZs, which leads to large errors in classification. To address this problem, this article proposes a parcel-based method for LCZ classification using Sentinel-2 images, road networks, and elevation data. First, the Sentinel-2 images are segmented by the road network to obtain the land parcels as classification units. Second, each image parcel is standardized to match the training dataset, So2Sat LCZ42. Third, the trained convolutional neural network (CNN) is used to classify the standardized parcels into LCZs. Finally, the building height information derived from elevation data is used to refine the LCZs by a rule-based classifier. The results of the four test sites show that the overall accuracy of our method is 0.75, higher than the sliding-window-based method's accuracy of 0.47. Additional simulation experiments demonstrated that parcels derived from road networks can reduce the mixture effect in image patches, and parcel standardization can ensure the transferability of the CNN model trained by regular image patches. Considering that the road network and elevation data are widely available, the proposed method has the potential of mapping LCZs in large areas.