With the increasing penetration of distributed energy resources and the wide distribution of access point, the power grid is becoming more and more weak. For the two main stability control strategies in weak grid, namely the current source grid connected mode (CSM) and the voltage source grid connected mode (VSM), the static characteristics of the power transmission are analyzed in this paper, respectively. In addition, through small signal modeling and analysis of the inverter operating at VSM, the stability and dynamic performance are improved when the grid impedance increases. Furthermore, it is concluded that the inverter is more suitable for operating at VSM in the larger grid impedance occasions. On the basis of the above analysis, this paper proposes the grid impedance adaptation dual mode control strategy in weak grid: when the grid impedance is low, the inverter operates at CSM, and when the grid impedance is large, the inverter operates at VSM. At last, the validity of the above analysis and the feasibility of the proposed scheme are verified by simulation and experiment.