We investigated near-field optical properties and images of single gold nanorods by using a near-field optical microscope. Observed transmission spectra show distinct transverse and longitudinal surface plasmon resonances. Transmission images observed near the surface plasmon resonances agree qualitatively with calculated maps of optical local density-of-states, and are assignable to plasmon wavefunctions. Ultrafast temporal responses in the single gold nanoparticles were observed by combining a near-field microscope with time-resolved techniques. Observed transient transmission images of the single nanorods show characteristic optical features, and are in good agreement with a calculated map of variation of local density of states arising from the elevation of electronic temperature in the nanorod induced by photoexcitation.