Abstract: As the penetration rate of distributed energy increases,the grid becomes weaker and weaker.Considering that the equivalent grid impedance of the grid-connected inverter access point in a weak grid tends to be changed by some factors,such as the line impedance,number of grid-connected inverters,loads,and the system operation mode,etc.It is aimed at the two main types of the inverter grid-connected control mode,i.e.current source mode（CSM） and voltage source mode（VSM）,from the relationship between monotonicity and damping characteristics of power transmission and grid impedance,the grid impedance stable operation boundary of CSM and VSM modes is derived in this paper.The grid impedance adaptation dual mode grid-connected stability control strategy in a weak grid is proposed.when the grid impedance is small,the inverter operates at CSM,and when the grid impedance is large,the inverter switches to operate at VSM,it will make the inverter operating stably over a wider range of grid impedance variations.A seamless switching scheme between CSM and VSM is also proposed in this paper,and the effectiveness of the above analysis and the feasibility of the proposed control strategy are verified by experiment.