Deep　learning　(DL)　has　emerged　as　a　powerful　tool　for　predicting　the　remaining　useful　lifetime　(RUL)　of　components　and　systems.　However,　there　are　two　challenges.　First,　DL-based　methods　require　a　sufficient　number　of　labelled　samples,　while　the　number　of　run-to-failure　units　in　practical　is　often　small　due　to　the　high　cost　and　time-consuming　life　test.　Second,　it　is　desirable　to　provide　the　prediction　uncertainty　of　RUL　for　maintenance　decision-making.　To　tackle　above　issues,　we　propose　a　novel　few-shot　RUL　prediction　model　with　a　hypernetwork　structure　incorporating　uncertainty　quantification　and　calibration　(Hyper-UC).　The　proposed　Hyper-UC　uses　a　shared　feature　embedding　network　and　a　unit-specific　weight　to　model　the　mapping　from　sensor　signals　to　RUL,　and　a　generative　network　is　designed　to　learn　the　meta-knowledge　of　generating　distributions　over　the　unit-specific　weights.　To　accurately　provide　the　predictive　uncertainty,　the　Hyper-UC　systematically　models　two　types　of　uncertainty:　epistemic　uncertainty　and　aleatoric　uncertainty.　In　the　online　phase,　the　unit-specific　weights　of　in-service　units　are　obtained　through　calibration,　and　subsequently　the　predictive　distribution　of　the　RUL　can　be　obtained.　The　proposed　method　is　evaluated　to　have　superior　model　performance　than　the　benchmark　methods　in　a　case　study　using　the　C-MAPSS　dataset.　©　2024　IEEE.