The oil displacement characteristics of CO2 in low permeability heterogeneous multi-layer reservoirs are different from those in single-layer reservoirs. To clarify the CO2 flooding characteristics in heterogeneous multi-layer reservoirs，we simulated the CO2 flooding process in low permeability heterogeneous multi-layer reservoirs through the displacement experiments with three pipes of long core in parallel connection. The oil displacement efficiency of high，medium and low permeability layers after continuous CO2 flooding and water-alternating-gas（WAG）flooding were evaluated under immiscible and miscible pressures. The damage characteristics of asphaltene precipitation to heterogeneous multi-layer reservoirs were clarified. The results reveal that continuous injection of CO2 under immiscible or miscible pressures will lead to the rapid breakthrough of the high permeability layer，and the breakthrough of CO2 under miscible pressure is earlier than that under immiscible pressure. After the breakthrough，the contribution rate of the high permeability layer to the total recovery factor is more than 91.7%，while those of the medium permeability layer under immiscible and miscible pressure are 5.6% and 2.1%，and that of the low permeability layer is 0. After CO2 flooding is converted to WAG flooding，the swept volume of CO2 increases significantly，and the recovery factors of medium and low permeability layers are improved considerably. However，the medium and low permeability layers still represent the main direction for tapping the reservoir potential in the later stage. Under miscible pressure，the damage of asphaltene precipitation to heterogeneous multi-layer reservoirs mainly concentrates in the rear of the high permeability layer，near the outlet；while under immiscible pressure，it is mainly in the front and middle of the high permeability layer，near the inlet，but the degree of damage is lower than that under miscible pressure. The influence of asphaltene precipitation on the medium and low permeability layers can be ignored.