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Strain effects on Josephson current in a graphene-superconductor junction are explored theoretically. It is demonstrated that the supercurrent is an oscillatory function of zigzag direction strain with a strain-dependent oscillating frequency. Interestingly, it is found that the Josephson current under armchair direction strain can be turned on/off with a cutoff strain. In view of the on/off properties of the Josephson current, we propose the strained graphene Josephson junction to be utilized as a supercurrent switch.