Satellite-based communication technology regains much attention in the past few years, where the satellites mainly play the role as relay devices to the communication networks. In this article, we focus on the data storage leveraging the low-Earth-orbit satellite-based data center (also called space-based cloud), which has been considered as a very promising secure paradigm for data storage, especially in the big data era. We first propose a layered architecture for the space-based cloud infrastructure. Then a novel management framework is devised to enable the operability of the proposed architecture. Finally, some challenging open issues are revealed from both the academic and industrial perspectives.