Two-dimensional (2D) layered hybrid perovskites of (RNH3)2PbX4 (R is an alkyl and X is a halide) have been recently synthesized and exhibited rich optical properties including fluorescence and exciton effects. However, few studies on transport and optoelectronic measurements of individual 2D perovskite crystals have been reported, presumably owing to the instability issue during electronic device fabrications. Here we report the first photodetector based on individual 2D (C4H9NH3)2PbBr4 perovskite crystals, built with the protection and top contact of graphene film. Both a high responsivity (∼2100 A/W) and extremely low dark current (∼10-10 A) are achieved with a design of interdigital graphene electrodes. Our study paves the way to build high-performance optoelectronic devices based on the emerging 2D single-crystal perovskite materials.