H.E.S.S. is an array of five Imaging Atmospheric Cherenkov Telescopes (IACTs) located 1800 m above sea level in the Khomas Highland of Namibia and is sensitive to very-high-energy (VHE) gamma rays between tens of GeV to tens of TeV. The very-high background rejection capabilities of IACTs provide excellent sensitivity of H.E.S.S. to GRBs. In this contribution the status of the H.E.S.S. GRB programme, already started in 2003, is reviewed. A highlight is the recent addition of the fifth telescope, which is the world's largest IACT. Its 600 square metre mirror lowers the energy threshold to tens of GeV and provides an effective area that is ten thousands of times larger than Fermi-LAT at these energies. The higher performance drive system will reduce the response time to a GRB alert, which will significantly enhance the chances of a H.E.S.S. GRB detection. Recent results on selected GRBs will be shown.