Gamma-ray bursts (GRBs) are the most powerful events in the universe, and are promising standard candles for cosmological studies. The data from NASA's Swift satellite reveal a distribution for the GRB number density that peaks at a redshift between 1 and 3. In this paper, we classify GRBs based on their duration and discuss the origin of their progenitors. We shed light on the formation mechanism of supermassive black holes and massive stars at the early universe, and show how this process and other related events can lead to a relatively high number of GRBs that peak at high redshift.