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Counter propagated write and read lasers can be used to generate non-classical correlated photon pairs in an atomic ensemble.We experimentally investigate how the detuning of the write laser affects the non-classical correlation function between the Stokes photon and the anti-Stokes photon,which are generated via a spontaneous four-wave mixing process using an off-axis configuration in a cold 85Rb atomic ensemble.The change of the time-resolved second-order correlated function between the Stokes and anti-Stokes photons is presented.The experimental result suggests that a suitable choice of detuning should be considered in such an experiment.