Complex of cerium (III) with (E)-N-benzylidene-4-methoxyaniline is synthesized through a one-pot three-component reaction from aromatic aldehyde, aromatic amine and the CeCl 3 · 7 H 2 O, as an efficient catalyst. This cerium (III) complex is characterized by IR, 1H, and 13C NMRspectroscopy and mass-spectral data. Molecular structure, Mullikan charges, thermodynamic parameters; vibrational frequencies and intensities were calculated by Density Functional theory methods (B3LYP, B3PW91, mPW1PW91 and PBEPBE) using the SDD basis set. The comparison between the calculated and experimental data in order to attain the best quality and to predict the structure, the best performance in the vibration spectra perfected of the title compound, we have found that the harmonic vibration computed are in a good agreement with the observed in IR spectrum, for closest match we calculated optimal scaling factors can recommend for the IR spectral future predictions for unknown compounds of this class. In order to better comparison, we also root mean square values of the experimental and calculated IR bands are 16.64, 16.64, 17.45, 17.66 and the mean absolute percentage error values are 1.33, 1.39, 1.40, and 1.5 for B3LYP, B3PW91, mPW1PW91, and PBEPBE methods respectively.