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Space cooling consumes large amounts of electricity, and the market-dominant vapor-compression refrigeration relies on high global-warming-potential refrigerants. Elastocaloric cooling using shape memory alloys is a promising alternative because of its high energy efficiency and greenhouse-gas-free properties. However, the limited system temperature span and cooling power in existing elastocaloric devices restrict the commercialization of this technology. We address the challenge by designing and fabricating a tubular NiTi of spiral cross-section to increase the specific heat transfer area and by developing a cascade-unit architecture to increase the length of the regenerator without Euler buckling under compression. In terms of the temperature span and cooling power metrics, our device surpasses those of all existing elastocaloric devices, demonstrating a great potential for space cooling in the near future.