A driving support apparatus that stores travel data while a driver causes a vehicle to travel by performing a driving operation and performs a driving support based on the stored travel data, the apparatus comprising: a storage unit that stores a vehicle speed at each position on a traveling route using the vehicle speed acquired when the driver causes the vehicle to travel by performing an acceleration or deceleration operation; a position acquisition unit that acquires a current position of the vehicle; and a traveling control unit that performs a traveling control based on the vehicle speed at each position stored in the storage unit and the current position of the vehicle acquired by the position acquisition unit, wherein, in a case where the vehicle speed of the vehicle becomes lower than a threshold value during the deceleration by the traveling control, the traveling control unit ends the traveling control, characterized in that the traveling control unit ends the traveling control before the vehicle reaches a stop position where the vehicle speed stored in the storage unit becomes zero km/h; the driving support apparatus further comprising: an acceleration request detection unit that detects an acceleration request from the driver, wherein, in a case where the acceleration request is detected by the acceleration request detection unit before the vehicle speed of the vehicle becomes lower than the threshold value during the deceleration control by the traveling control, the traveling control unit performs the traveling control while excluding the vehicle speed lower than the vehicle speed at the time of detecting the acceleration request among the vehicle speed data before and after the stop position stored in the storage unit. a storage unit that stores a vehicle speed at each position on a traveling route using the vehicle speed acquired when the driver causes the vehicle to travel by performing an acceleration or deceleration operation; a position acquisition unit that acquires a current position of the vehicle; and a traveling control unit that performs a traveling control based on the vehicle speed at each position stored in the storage unit and the current position of the vehicle acquired by the position acquisition unit, wherein, in a case where the vehicle speed of the vehicle becomes lower than a threshold value during the deceleration by the traveling control, the traveling control unit ends the traveling control, characterized in that the traveling control unit ends the traveling control before the vehicle reaches a stop position where the vehicle speed stored in the storage unit becomes zero km/h; the driving support apparatus further comprising: an acceleration request detection unit that detects an acceleration request from the driver, wherein, in a case where the acceleration request is detected by the acceleration request detection unit before the vehicle speed of the vehicle becomes lower than the threshold value during the deceleration control by the traveling control, the traveling control unit performs the traveling control while excluding the vehicle speed lower than the vehicle speed at the time of detecting the acceleration request among the vehicle speed data before and after the stop position stored in the storage unit. an acceleration request detection unit that detects an acceleration request from the driver, wherein, in a case where the acceleration request is detected by the acceleration request detection unit before the vehicle speed of the vehicle becomes lower than the threshold value during the deceleration control by the traveling control, the traveling control unit performs the traveling control while excluding the vehicle speed lower than the vehicle speed at the time of detecting the acceleration request among the vehicle speed data before and after the stop position stored in the storage unit.