  Very-high-energy (VHE; >~100 GeV) gamma-rays are expected from gamma-ray
bursts (GRBs) in some scenarios. Exploring this photon energy regime is
necessary for understanding the energetics and properties of GRBs. GRBs have
been one of the prime targets for the H.E.S.S. experiment, which makes use of
four Imaging Atmospheric Cherenkov Telescopes (IACTs) to detect VHE gamma-rays.
Dedicated observations of 32 GRB positions were made in the years 2003-2007 and
a search for VHE gamma-ray counterparts of these GRBs was made. Depending on
the visibility and observing conditions, the observations mostly start minutes
to hours after the burst and typically last two hours. Results from
observations of 22 GRB positions are presented and evidence of a VHE signal was
found neither in observations of any individual GRBs, nor from stacking data
from subsets of GRBs with higher expected VHE flux according to a
model-independent ranking scheme. Upper limits for the VHE gamma-ray flux from
the GRB positions were derived. For those GRBs with measured redshifts,
differential upper limits at the energy threshold after correcting for
absorption due to extra-galactic background light are also presented.
