A driving support apparatus for a vehicle comprising a steering device that steers steerable wheels, and a control unit configured to execute a running control in which a steered angle of the steerable wheels is changed by controlling the steering device, the control unit being configured to calculate a deviation between an index value of a target running state of the vehicle and an index value of an actual running state, to calculate a target change amount of the steered angle based on the index value deviation, to control the steering device so that a change amount of the steered angle conforms to the target change amount, and to limit a magnitude of a time change rate of the steered angle changed by the running control when one of a magnitude of the index value deviation and a magnitude of the target change amount exceeds a reference value.