We propose a kind of plasmonic whispering-gallery mode highly localized on the exterior surface of a metal-coated microresonator. This exterior (EX) surface mode possesses high quality factors at room temperature, and can be efficiently excited by a tapered fiber. The EX mode can couple to an interior (IN) mode and this coupling produces a strong anticrossing behavior, which not only allows conversion of IN to EX modes, but also forms a long-lived antisymmetric mode. As a potential application, the EX mode could be used for a biosensor with a sensitivity high of up to 500 nm per refraction index unit, a large figure of merit, and a wide detection range.