The structural, electronic and vibrational properties of solid carbon dioxide phases (I, II, III, and IV) under high pressure are studied using first-principles calculations. The calculated structural parameters are in good agreement with the experimental values. The third-order Birch-Murnaghan equation of state is fitted, and the corresponding parameters are obtained. We obtained the phase boundary points of each phase and plotted the phase diagram of solid carbon dioxide. The influence of pressure on the band structure and density of states is studied. The vibrational properties of the four phases of carbon dioxide were studied in detail, and the infrared and Raman spectra of the four phases were obtained. It can be seen from the calculated spectrum that the number and frequency of vibration peaks are in good agreement with the experimental values. And, we also analyze the influence of pressure on the frequency of vibration mode.