Based on the ligand H4Salen-8tBu (salen-4), a new dinuclear cobalt complex (salen-4)[Co(III)TFA]2 (salen-4 = 3,5-di-tert-butylsalicylaldehyde-3,3′-diaminobiphenylamine; TFA = trifluoroacetic acid) has been firstly synthesized and characterized. It shows high catalytic activity for the copolymerization of propylene oxide (PO) and carbon dioxide (CO2), yielding regioregular poly(propylene carbonate) (PPC) with little generation of propylene carbonate (PC) by-product. It has been found that (salen-4)[Co(III)TFA]2 shows higher activity at milder conditions, generating a polymer with maximum Mn of 293 kg/mol and a narrow molecular weight distribution PDI of 1.35. The influences of reaction time, CO2 pressure, reaction temperature, nature of the cocatalyst, catalyst dosage and substrate concentration on the molecular weight, yield and selectivity of the polymer were explored in detail. The results showed that the (salen-4)[Co(III)TFA]2/[PPN]TFA catalyst system demonstrated a remarkable TOF as high as 735 h–1. In addition, a hypothetical catalytic reaction mechanism was proposed based on density functional theory (DFT) calculations and the catalytic reaction results of the (salen-4)[Co(III)TFA]2.