Precise knowledge of nuclear interactions with the detector materials is crucial for the accurate measure- ments of cosmic-ray nuclei fluxes. We have measured the interaction cross sections on carbon target for various nuclear species with charge 2≤Z≤16 in a wide rigidity (momentum/charge) range from a few GV to TV, using cosmic-ray nuclei events collected by the Alpha Magnetic Spectrometer. The properties of the measured nuclear interaction cross sections are discussed.