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The phonon-assisted quantum cutting (PQC) model is presumed to clarify the red up-conversion luminescence process in Er3+ /Yb3+ co-doped glass ceramics by the excitation and emission spectra. The red up-conversion luminescence of Er3+ ions mainly comes from three-photon absorption by the PQC process when the rare earth ions are doped in the glass ceramics and excited by 980nm pumped-laser. Er3+ ions absorb three-photons and relax to the 4G11/2 state and then emit red up-conversion luminescence by the PQC process. The factor coefficient for the relation of pump-laser power and up-conversion intensity (P-I) is found by the analysis of excitation spectra of the red luminescence, which plays a major role to understand the true red up-conversion luminescence process. The new P-I relation is explained by the model of PQC.