Surface plasmons, the quanta of the collective oscillations of free electrons at metal surface, can be easily tuned by changing the surrounding dielectric materials, which is well known for metal nanoparticles and metal surfaces, but less is known for one-dimensional metal nanowires. Here, we find an extremely large tunability of surface plasmons on Ag nanowires with a beat period of the near-field distribution pattern increasing by 90 nm per nanometer of Al2O3 coating, or by 16 µm per refractive index unit change in the surrounding medium. Such high sensitivity is crucial to directly control the optical signal distribution for various routing and demultiplexing functions in plasmonic circuits and may pave the way to the development of on-chip ultrasensitive biosensing.