We investigated near-field optical properties of single gold nanorods with spatial resolution down to 50 nm. Gold nanorods show transverse and longitudinal surface plasmon resonances in visible and near-infrared region, respectively. Transmission images observed near the resonances agree qualitatively with calculated electromagnetic local density of states, and are reflected by spatial characteristics of plasmon eigenfunctions. Ultrafast temporal responses of local density of states have been imaged by combining near-field microscope with time-resolved technique. It has been found that dynamic behavior of surface plasmon in the center of the rod is different from that in the both ends.