A multi-detector telescope has started functioning at Gulmarg, India, to study cosmic gamma-ray sources at photon energies beyond 1012 eV, through the mode of atmospheric Cerenkov radiation. The authors describe the instrumentation details of the Gulmarg telescope and also present an account of the telescope performance under actual observation conditions. An estimate of the telescope sensitivity, in terms of the minimum observation time required to detect a statistically significant signal from several representative gamma -ray sources, is also given.