Quantum electrodynamics describes the interactions of electrons and photons. Electric charge (the gauge coupling constant) is energy dependent, and there is a previous claim that charge is affected by gravity (described by general relativity) with the implication that the charge is reduced at high energies. However, that claim has been very controversial and the matter has not been settled. Here I report an analysis (free from the earlier controversies) demonstrating that quantum gravity corrections to quantum electrodynamics have a quadratic energy dependence that result in the electric charge vanishing at high energies, a result known as asymptotic freedom.