An apparatus for determining the critical points and phase behavior is described. The apparatus was used to investigate the phase behavior of pure CO2 and the ternary mixture of CH3OH + CO + CO2. The critical points were obtained from both the critical opalescence and the isothermal compressibility. The critical temperature and critical pressure of CO2, determined by this method, agreed well with literature values. The critical points and the homogeneous points of the ternary mixtures were determined in the CO2-rich region.