Euphorbia otjingandu Swanepoel, here described as a new species, is a robust succulent tree only known from the Namibian part of the Kaokoveld Centre of Endemism. Its range is likely to extend into adjacent mountainous regions of southwestern Angola. Illustrations of the plant and a distribution map are provided. Diagnostic characters of the new species include the short trunk, the succulent, spiny, 4–8-winged, conspicuously segmented branches and the flat-topped candelabriform habit. A table with diagnostic morphological features to distinguish among the new species, its suggested nearest relative E. fortissima Leach, and several other species with which it can be confused, is provided.