The phase transitions among the high-pressure polymorphic forms of CaCO3 (cc-I, -II, -III, and -IIIb) were investigated by dynamic diamond anvil cell (dDAC) and in situ Raman spectroscopy.  Experiments were carried out at room temperature and high pressures up to 12.8 GPa with the pressurizing rate varied from 0.006 to 0.056 GPa/s.  In situ observation shows that with the increase of pressure, calcite transforms from cc-I to cc-II at ~1.5 GPa and from cc-II to cc-III at ~2.5 GPa, and transitions are independent of the pressurizing rate.  Further, as the pressure continues to increase, cc-IIIb begins to appear and coexists with cc-III within a pressure range that is inversely correlated to the pressurizing rate.  At the pressurizing rates of 0.006, 0.012, 0.021, and 0.056 GPa/s, the coexistence pressure ranges of cc-III and cc-IIIb are 2.8-9.8, 3.1-6.9, 2.7-6.0, and 2.8-4.5 GPa, respectively.  The dependence of the coexistence on pressurizing rate may result from the influence of pressurizing rate on activation process of transition by reducing energy barrier.  The higher the pressurizing rate, the lower the energy barrier, and the easier it is to pull the system out of the coexistence state.  The results of this in situ study provide new insights into understanding the phase transition of calcite.