We experimentally establish a non-classical correlation between a single Stokes photon and the collective spin excited state of a cold atomic ensemble by using a spontaneous Raman scattering process. The correlation between them can be proved by transferring the spin excited state of the atomic ensemble into an anti-Stokes photon and checking the Cauchy-Schwarz inequality between the Stokes and the anti-Stokes photons. The non-classical correlation can be kept for at least 300 ns.