The stator of doubly fed induction generator（DFIG） should be kept connection to the grid during the low voltage ride-through（LVRT） period. The flux dynamic response and rotor overvoltage induced by the grid voltage dip and recovery threaten to damage the vulnerable rotor converter， even cause LVRT failure. This paper uses dynamic model of DFIG， and proposes a method to analyze the motor dynamic responses respectively by use of positive and negative components under unsymmetrical grid voltage dips. The motor dynamic response is described by the stator flux vector locus and rotor voltage vector locus. The steady rotor overvoltage under unsymmetrical grid voltage is given. The maximum and minimum rotor overvoltage induced by the different time of grid voltage dip and recovery are well represented. The results of simulation to a DFIG system validate the proposed theoretical analysis. At last， a design method of the active Crowbar resistor is proposed.