Recently, a conceptually new physics beyond the standard model (SM), unparticle, has been proposed, where a hidden conformal sector is coupled to the SM sector through higher dimensional operators. In this setup, we investigate unparticle physics at the photon collider, in particular, unparticle effects on the gamma gamma ->gamma gamma process. Since this process occurs at loop level in the SM, the unparticle effects can be significant even if the cutoff scale is very high. In fact, we find that the unparticle effects cause sizable deviations from the SM results. The scaling dimension of the unparticle d(u) reflects the dependence of the cross section on the final state photon invariant mass, so that precision measurements of this dependence may reveal the scaling dimension of the unparticle.