The present invention relates to a system and method for controlling a minimum flow rate of a variable geometry turbocharger that improve the starting performance of a vehicle and prevent the generation of surge noise and smoke remarkably, comprising a stopper to restrict the lever rotation of a flow regulator and determine a minimum flow rate of the turbocharger based on the position that restricts the lever rotation, in a structure where its position can be regulated to control the lever rotation limit position and the minimum flow rate of the turbocharger, and an ECU to calculate a stopper position correction value, with which an actual boost pressure detected by a boost pressure detection unit satisfies a target boost pressure, if meeting predetermined vehicle speed and gear ratio conditions, and then to duty-control a stopper position regulator to correct the current stopper position by the calculated stopper position correction value.