An engine stop control system for a hybrid electric vehicle including a powertrain having an engine, an electric motor/generator, and driving wheels, including a first clutch coupling the engine to the motor/generator, a second clutch coupling the motor/generator to the driving wheels, a controller configured to select between two driving modes of the vehicle by controlling engagement and disengagement of the first clutch and the second clutch so that the vehicle may be driven either solely by the motor/generator or a combination of the engine and the motor/generator, and to control the stop position of the engine to be a desired stop position by controlling the rotation speed of the motor/generator while the first clutch in complete engagement and the second clutch in a slip state.