An apparatus and a method estimate backlash and compliance. The apparatus and the method are configured to distinguish and determine the backlash and the compliance occurring in a vehicle driving system. The method includes providing information related to a driving system model between a motor and a driving wheel for driving a vehicle to a controller, determining a compliance speed, by the controller, by using the information related to the driving system model based on vehicle driving information acquired by a driving information detector while the vehicle is driven, and determining a backlash speed, by the controller, by subtracting the determined compliance speed from an overall speed difference that is a difference between a motor speed and a driving wheel speed. The apparatus is configured to perform the method.