  In this paper, we investigate whether it is possible to determine the
neutrino mass hierarchy via a high-statistics and real-time observation of
supernova neutrinos with short-time characteristics. The essential idea is to
utilize distinct times-of-flight for different neutrino mass eigenstates from a
core-collapse supernova to the Earth, which may significantly change the time
distribution of neutrino events in the future huge water-Cherenkov and
liquid-scintillator detectors. For illustration, we consider two different
scenarios. The first case is the neutronization burst of $\nu^{}_e$ emitted in
the first tens of milliseconds of a core-collapse supernova, while the second
case is the black hole formation during the accretion phase for which neutrino
signals are expected to be abruptly terminated. In the latter scenario, it
turns out only when the supernova is at a distance of a few Mpc and the
fiducial mass of the detector is at the level of gigaton, might we be able to
discriminate between normal and inverted neutrino mass hierarchies. In the
former scenario, the probability for such a discrimination is even less due to
a poor statistics.
