We have investigated optical properties of single gold nanorods by using an apertured-type scanning near-field optical microscope. Near-field transmission spectrum of single gold nanorod shows several longitudinal surface plasmon resonances. Transmission images observed at these resonance wavelengths show oscillating pattern along the long axis of the nanorod. The number of oscillation increases with decrement of observing wavelength. These spatial characteristics were well reproduced by calculated local density-of-states maps and were attributed to spatial characteristics of plasmon modes inside the nanorods. Dispersion relation for plasmons in gold nanorods was obtained by plotting the resonance frequencies of the plasmon modes versus the wave vectors obtained from the transmission images.