A new method for measuring the wavelength dependence of the transit time, material dispersion, and attenuation of an optical fiber is described. The authors inject light from a 4-ns risetime pulsed broad-band flashlamp into various length fibers and record the transmitted signals with a time-resolved spectrograph. Segments of data spanning an approximately 3,000 {angstrom} range are recorded from a single flashlamp pulse. Comparison of data acquired with short and long fibers enables the determination of the transit time and the material dispersion as functions of wavelength dependence for the entire recorded spectrum simultaneously. The wavelength dependent attenuation is also determined from the signal intensities. The method is demonstrated with experiments using a step index 200-{micro}m-diameter SiO{sub 2} fiber. The results agree with the transit time determined from the bulk glass refractive index to within {+-} 0.035% for the visible (4,000--7,200 {angstrom}) spectrum and 0.12% for the ultraviolet (2,650--4,000 {angstrom}) spectrum, and with the attenuation specified by the fiber manufacturer to within {+-} 10%.