The influence of night-sky background on detecting cosmic gamma-ray bursts and measurements of their light curves with ground-based Cherenkov telescopes in the range between 1 and 10 GeV is considered. It is shown that the probability of registration of Cherenkov flashes from cosmic gamma-quanta decreases significantly at energies less than 3 GeV under the influence of night sky optical background even if the sensitivity of detecting units is better than that of modern Cherenkov telescopes.