If the ordinary neutrinos oscillate into a sterile flavor in a manner consistent with the Super-Kamiokande data on the zenith-angle dependence of atmospheric mu-neutrino flux, an energy sufficient to power a typical cosmic gamma-ray burst (GRB) (about 10^{52} erg) can be carried by sterile neutrinos away from the source and deposited in a region relatively free of baryons. Hence, ultra-relativistic bulk motion (required by the theory of and observations of GRBs and their afterglows) can easily be achieved in the vicinity of plausible sources of GRBs. Oscillations between sterile and ordinary neutrinos would thus provide a solution to the ``baryon-loading problem'' in the theory of GRBs.