Developing rapidly in recent years, smart home could integrate health care with ambient assisted living (AAL) technologies and provide activities of daily life (ADLs) to the people who need care. In this paper, we propose a smart home and cross-cloud-and-edge computing based nursing system (NS). In general, a good NS requires low latency, high stability, and the real-time analysis and response, where the conventional centralized cloud computing based approaches cannot meet those requirements very well. To this end, we introduce a novel distributed joint edge-cloud structure to better satisfy these requirements. Moreover, to deal with the privacy issue, we introduce the differential-privacy (DP) in the NS to protect the healthcare takers’ data privacy. In a word, we propose a privacy-preserving context-aware multi-armed bandit based online learning approach for edge-cloud-enabled NS in smart home. Additionally, our system with a novel top-down expanding tree based structure can support dynamically increasing health care datasets. Extensive simulation results demonstrate that the proposed solution can achieve accurate recommendation results.