We study the electron-photon deep inelastic scattering at small Bjorken variable $x$ in the framework of holographic QCD, employing the Pomeron exchange to describe the involved strong interaction. With the Brower-Polchinski-Strassler-Tan Pomeron exchange kernel and appropriate wave functions for the incident and target particles, which are defined in the five-dimensional AdS space, we obtain the photon structure functions. It is shown that our predictions agree with the experimental data measured at LEP and with those derived from a known parameterization of the photon parton distribution functions.