We have demonstrated a Fourier-domain optical coherence tomography (FD-OCT) scheme with a high-speed frequency-swept light source based on a chirped supercontinuum pulse. Instead of using a swept laser, an ultra-wideband supercontinuum pulse was chirped or stretched in the time domain by using a long dispersive single-mode optical fiber by the help of the group velocity dispersion. The chirped pulse was used directly as frequency-swept light for OCT after measuring the relationship between the time delay and the wavelength. Very high acquisition speeds up to 5-MHz in A-line scan rate were achieved because there is no speed-limiting moving part in this scheme. And high resolution up to 3.6 um in air was enabled owing to the use of wideband supercontinuum. It was shown that the scheme does not require re-calibration of the sweep characteristics because the sweeping mechanism is passive and stable.