As highly intensive and brief pulses of light, gamma-ray bursts (GRBs) are the most energetic explosive phenomena in the Universe. A few mechanisms could explain the production of some GRB emissions, however, the physical origin of GRBs especially the high-energy (more than one GeV) and very-high-energy (above 100 GeV) ones still remains largely unknown. Based on our previously revealed quantitative relation between the speed of light in vacuum c and the temperature T of cosmic microwave background (CMB), we propose that the mass-energy relation at the redshift z space-time in the Universe should be E=mc2(1+z)2. Then, the mass-loss events such as the annihilation of matter and antimatter at high-redshift space-time will produce more energetic gamma-rays than our present space-time. Finally, we confirmed that this theoretical model is highly compatible with both the observed data and an empirical formula E_iso∝〖(1+z)〗^(〖1.80〗_(-0.63)^(+0.36) ). These results suggest that the events of mass-energy transition such as matter and antimatter collision at distant space-time in the Universe could be a possible physical origin of GRBs including the high-energy and the very-high-energy ones.