A driving support apparatus for a vehicle provided with an object detecting apparatus (21, 22) that is configured to detect an object surrounding an own vehicle, the driving support apparatus performing a driving support control with respect to a preceding vehicle running ahead of the own vehicle based on detection information, the driving support apparatus comprising: an other vehicle determination unit that is configured to determine whether or not a moving state is present in which an other vehicle in an adjacent lane adjacent to a present lane where the own vehicle runs, moves towards the present lane; an acquiring unit that is configured to acquire, based on the detection information of the object detecting apparatus, a tip end lateral position of the other vehicle in a present lane side, among lateral positions of the other vehicle in a direction perpendicular to a travelling direction of the own vehicle; the driving support apparatus being characterized by further comprising: a portion determination unit that is configured to determine whether the tip end lateral position of the other vehicle acquired by the acquiring unit is a lateral position of a portion other than a front end portion of the other vehicle; an estimation unit that is configured to estimate, when the portion determination unit determines the lateral position of a portion other than a front end portion of the other vehicle, a front end lateral position of the other vehicle, based on a travelling direction of the other vehicle, a lateral position of the other vehicle, and length information in a front-rear direction of the other vehicle; and an object determination unit configured to, when the other vehicle determination unit determines that the moving state is present, determine based on a movement or a predicted movement of the front end lateral position into the present lane from the adjacent lane, the other vehicle to be an object of a driving support control, and determine based on no-movement of the front end lateral position into the present lane, the other vehicle not to be an object of a driving support control. an other vehicle determination unit that is configured to determine whether or not a moving state is present in which an other vehicle in an adjacent lane adjacent to a present lane where the own vehicle runs, moves towards the present lane; an acquiring unit that is configured to acquire, based on the detection information of the object detecting apparatus, a tip end lateral position of the other vehicle in a present lane side, among lateral positions of the other vehicle in a direction perpendicular to a travelling direction of the own vehicle; the driving support apparatus being characterized by further comprising: a portion determination unit that is configured to determine whether the tip end lateral position of the other vehicle acquired by the acquiring unit is a lateral position of a portion other than a front end portion of the other vehicle; an estimation unit that is configured to estimate, when the portion determination unit determines the lateral position of a portion other than a front end portion of the other vehicle, a front end lateral position of the other vehicle, based on a travelling direction of the other vehicle, a lateral position of the other vehicle, and length information in a front-rear direction of the other vehicle; and an object determination unit configured to, when the other vehicle determination unit determines that the moving state is present, determine based on a movement or a predicted movement of the front end lateral position into the present lane from the adjacent lane, the other vehicle to be an object of a driving support control, and determine based on no-movement of the front end lateral position into the present lane, the other vehicle not to be an object of a driving support control. a portion determination unit that is configured to determine whether the tip end lateral position of the other vehicle acquired by the acquiring unit is a lateral position of a portion other than a front end portion of the other vehicle; an estimation unit that is configured to estimate, when the portion determination unit determines the lateral position of a portion other than a front end portion of the other vehicle, a front end lateral position of the other vehicle, based on a travelling direction of the other vehicle, a lateral position of the other vehicle, and length information in a front-rear direction of the other vehicle; and an object determination unit configured to, when the other vehicle determination unit determines that the moving state is present, determine based on a movement or a predicted movement of the front end lateral position into the present lane from the adjacent lane, the other vehicle to be an object of a driving support control, and determine based on no-movement of the front end lateral position into the present lane, the other vehicle not to be an object of a driving support control.