We report dramatic reduction in plasmon resonance linewidth of a single Au nanorod by coupling it to a whispering gallery cavity of a silica microfiber. With fiber diameter below 6 μm, strong coupling between the nanorod and the cavity occurs, leading to evident mode splitting and spectral narrowing. Using a 1.46-μm-diameter microfiber, we obtained single-band 2-nm-linewidth plasmon resonance in an Au nanorod around 655-nm wavelength, with a quality factor up to 330 and extinction ratio of 30 dB. Compared to an uncoupled Au nanorod, the strongly coupled nanorod offers a 30-fold enhancement in the peak intensity of plasmonic resonant scattering.