The concept of the local climate zone (LCZ) has been recently proposed as a generic land-cover/land-use classification scheme. It divides urban regions into 17 categories based on compositions of man-made structures and natural landscapes. Although it was originally designed for temperature study, the morphological structure concealed in LCZs also reflects economic status and population distribution. To this end, global LCZ classification is of great value for worldwide studies on economy and population. Conventional classification approaches are usually successful for an individual city using optical remote sensing data. This paper, however, attempts for the first time to produce global LCZ classification maps using polarimetric synthetic aperture radar (PolSAR) data. Specifically, we first produce polarimetric features, local statistical features, texture features, and morphological features and compare them, with respect to their classification performance. Here, an ensemble classifier is investigated, which is trained and tested on already separated transcontinental cities. Considering the challenging global scope this work handles, we conclude the classification accuracy is not yet satisfactory. However, Sentinel-1 dual-Pol SAR data could contribute the classification for several LCZ classes. According to our feature studies, the combination of local statistical features and morphological features yields the best classification results with 61.8% overall accuracy (OA), which is 3% higher than the OA produced by the second best features combination. The 3% is considerably large for a global scale. Based on our feature importance analysis, features related to VH polarized data contributed the most to the eventual classification result.