Deep　Convolution　Neural　Networks　(CNNs)　have　become　the　cornerstone　of　image　classification,　but　the　emergence　of　adversarial　image　attacks　brings　serious　security　risks　to　CNN-based　applications.　As　a　local　perturbation　attack,　the　border　attack　can　achieve　high　success　rates　by　only　modifying　the　pixels　around　the　border　of　an　image,　which　is　a　novel　attack　perspective.　However,　existing　border　attacks　have　shortcomings　in　stealthiness　and　are　easily　detected.　In　this　article,　we　propose　a　novel　stealthy　border　attack　method　based　on　deep　feature　alignment.　Specifically,　we　propose　a　deep　feature　alignment　algorithm　based　on　style　transfer　to　guarantee　the　stealthiness　of　adversarial　borders.　The　algorithm　takes　the　deep　feature　difference　between　the　adversarial　and　the　original　borders　as　the　stealthiness　loss　and　thus　ensures　good　stealthiness　of　the　generated　adversarial　images.　To　ensure　high　attack　success　rates　simultaneously,　we　apply　cross　entropy　to　design　the　targeted　attack　loss　and　use　margin　loss　as　well　as　Leaky　ReLU　to　design　the　untargeted　attack　loss.　Experiments　show　that　the　structural　similarity　between　the　generated　adversarial　images　and　the　original　images　is　8.8%　higher　than　the　state-of-art　border　attack　method,　indicating　that　our　proposed　adversarial　images　have　better　stealthiness.　At　the　same　time,　the　success　rate　of　our　attack　in　the　face　of　defense　methods　is　much　higher,　which　is　about　four　times　that　of　the　state-of-art　border　attack　under　the　adversarial　training　defense.