In this paper, we derived electromagnetic field transformations and electromagnetic field equations of Maxwell in Rindler space-time in the context of general theory of relativity. We then treat the Lorentz gauge transformation and the Lorentz gauge fixing condition in Rindler space-time and obtained the transformation of differential operation, the electromagnetic 4-vector potential and the field. In addition, charge density and the electric current density in Rindler spacetimeare derived. To view the invariance of the gauge transformation, gauge theory is applied to Maxwell equations in Rindler space-time. In Appendix A, we show that the electromagnetic wave function cannot exist in Rindler space-time. An important point we assert in this article is the uniqueness of the accelerated frame. It is because, in the accelerated frame, one can treat electromagnetic field equations.