Due to the great absorption of reactive power after voltage drops caused by faults in network, the low-voltage ride through (LVRT) capability of squirrel cage induction generators (SCIGs) in wind farms is a great challenge. If a static VAR compensator (SVC) is installed at the point of common coupling (PCC) of a wind farm with a main network, it can improve the wind generation's LVRT capability with reactive power compensation. In the voltage control loop of a conventional SVC, the voltage actual value of the PCC is compared with the reference voltage value. This paper presents a method for implementation of a SVC based on grey theory and fuzzy logic to improve the LVRT capability of SCIG wind turbines. In this method, instead of the voltage actual value of the PCC, the voltage of the PCC is predicted by the GM (1,1) grey model. Predicted voltage is then compared with reference voltage. After obtaining voltage error, a fuzzy controller with a PI controller in the SVC voltage control loop controls the SVC output. The simulation results are compared for a conventional SVC, fuzzy SVC and fuzzy-grey SVC. These results show the superiority of the fuzzy-grey controller for the SVC in improving the LVRT capability of wind farms with SCIGs.