Abstract: A grid-tied voltage source converter（VSC） system may suffer from instability problem when its connection with the grid is weak.This has been one of most concerned and important problems,pursued by many researchers in recent decade.This paper reviewed the research progress on the problem in three main aspects: modeling of the VSC-based system,methods of stability analysis and mechanism of loss of VSC-based system stability.Especially,the paper reviewed the three main factors that may affect the VSC-based system stability considerably.They are the effect of the phase locked loop（PLL）,dynamic interactions between the PLL and VSC control system,the case that the PLL was not considered.The paper was concluded with a short summary on the analytical methods,main results and conclusions obtained so far and issues to be addressed in the future.