The factor group symmetry analysis (FSA) method and position symmetry analysis (PSA) method are used to analyze the vibrational modes of calcite (CaCO3) crystal, respectively. With the activated results of infrared and Raman spectra presented, strong points of each method are concluded. The infrared spectra are studied by using dynamics calculations based on density-functional theory (DFT) with the supercell model of calcite crystal. The frequencies of 27 normal modes are achieved, which are consistent with that by the group symmetry analysis very well, and fit with the experimental results better than the lattice dynamical methods.