The constant speed of light is valid in the special relativity, but when we consider the a general relativistic metric according to the principle of equivalence, the possibility of the variation of the speed of light may not be ignored if it demanded to justify a property of the the gravitational field. The only problem is then arises is to modify the electromagnetic field equations on the basis of the variable speed of light with the requirement that the field equations reduces to the field equations of the special relativity when the speed of light tends to constant..