It　is　a　challenging　task　to　recognize　novel　categories　with　only　a　few　labeled　remote-sensing　images.　Currently,　meta-learning　solves　the　problem　by　learning　prior　knowledge　from　another　dataset　where　the　classes　are　disjoint.　However,　the　existing　methods　assume　the　training　dataset　comes　from　the　same　domain　as　the　test　dataset.　For　remote-sensing　images,　test　datasets　may　come　from　different　domains.　It　is　impossible　to　collect　a　training　dataset　for　each　domain.　Meta-learning　and　transfer　learning　are　widely　used　to　tackle　the　few-shot　classification　and　the　cross-domain　classification,　respectively.　However,　it　is　difficult　to　recognize　novel　categories　from　various　domains　with　only　a　few　images.　In　this　article,　a　domain　mapping　network　(DMN)　is　proposed　to　cope　with　the　few-shot　classification　under　domain　shift.　DMN　trains　an　efficient　few-shot　classification　model　on　the　source　domain　and　then　adapts　the　model　to　the　target　domain.　Specifically,　dual　autoencoders　are　exploited　to　fit　the　source　and　target　domain　distribution.　First,　DMN　learns　an　autoencoder　on　the　source　domain　to　fit　the　source　domain　distribution.　Then,　a　target　autoencoder　is　initiated　from　the　source　domain　autoencoder　and　further　updated　with　a　few　target　images.　To　ensure　the　distribution　alignment,　cycle-consistency　losses　are　proposed　to　jointly　train　the　source　autoencoder　and　target　autoencoder.　Extensive　experiments　are　conducted　to　validate　the　generalizable　and　superiority　of　the　proposed　method.