We design and demonstrate an all-optical temporal differentiator based on a simple Moire fiber grating operated in reflection. The simulation results prove that a single Moire fiber grating with only one \pi-phase shifted point can act as the first-order temporal differentiator and that a Moire fiber grating incorporating two symmetrical -phase shifted points can act as the second-order temporal differentiator. A practical Moire fiber grating is fabricated, thereby proving that such a grating can act as the first-order temporal differentiator. Our results verify the feasibility, flexibility, and accuracy of the proposed method.