The possibility that the Universe contains significant amounts of primordial black holes (PBHs) with a fraction of a solar mass (~ 1032 g or less) is not excluded at present. Although there are limits on the number of low-mass PBHs (m ~ 1015 g), there is some evidence for their existence. The abundance of PBHs is not inconsistent with the fluctuation density in the early Universe, especially near the time of the quark-gluon (Q-G) phase transition. We discuss a very interesting group of gamma-ray bursts (GRBs) of very short time duration and an increasing hard spectrum from the published BATSE catalog. We point out that the trend, i.e., anti-correlation of hardness ratio vs GRB duration, would be expected if some of the short GRBs came from black hole evaporation. We discuss the possibility that the onset of the Q-G plasma can give rise to such GRBs from PBH evaporation.