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Correlated photons are essential sources for quantum information processing. We propose a practical scheme to generate pairs of correlated photons in a controllable fashion from a double-cavity optomechanical system, where the variable optomechanical coupling strength makes it possible to tune the photon correlation at our will. The key operation is based on the repulsive or attractive interaction between the two photons intermediated by the mechanical resonator. The present protocol could provide a potential approach to coherent control of the photon correlation using the optomechanical cavity.