Mono-atomic-layer graphene is an interesting system for studying the relativistic carrier transport arising from a linear energy-momentum dispersion relation. An easy control of the carrier density in graphene by applying an external gate field makes the system even more useful. In this study, we measured the Josephson current in a device consisting of mono-layer graphene sheet sandwiched between two closely spaced (~300 nm) aluminum superconducting electrodes. Gate dependence of the supercurrent in graphene Josephson junction follows the gate dependence of the normal-state conductance. The gate-tunable and relatively large supercurrent in a graphene Josephson junction would facilitate our understanding on the weak-link behavior in a superconducting-normal metal-superconducting (SNS) type Josephson junction.