In this paper, we proposed and numerically demonstrated a novel method to effectively minimize Fresnel reflection from a perpendicularly cleaved fiber using a uniform fiber Bragg grating (FBG) inscribed at the fiber end. By matching the reflectivity of an in-line FBG with the reflectivity caused by the glass-air boundary, the FBG acts as a virtual boundary, which provides destructive interference and suppresses Fresnel reflection. We achieved an anti-reflection FBG with a return loss of more than 80 dB by ensuring that the product of the index contrast and grating period number is almost constant, with a value of 0.2695.