We describe an instrument for the time-resolved spectroscopy of turbid media that is based on supercontinuum generation in a photonic crystal fiber. The light injected into the sample consists of subpicosecond pulses that cover 550-1000 nm at 85 MHz at an average power of as much as 40 mW. A spectrometer coupled to a multianode photomultiplier tube is used to detect the light simultaneously in 16 wavelength channels, with a resolution of 5-20 nm/channel, depending on the grating. Time-correlated single-photon counting is used to produce time-dispersion curves, which one fits to the diffusion equation to determine absorption and reduced scattering coefficients. We tested the instrument by measuring the time-resolved diffuse reflectance of epoxy phantoms and by performing in vivo measurements on volunteers. The results were similar to those obtained with previous discrete wavelength systems, whereas the full spectrum (610-810 nm) acquisition time was as short as 1 s owing to the parallel acquisition.