A preceding vehicle selection apparatus estimates a curvature of a traveling road on which an own vehicle is traveling, detects an object ahead of the own vehicle, and determines a relative position in relation to the own vehicle, for each object ahead. Based on the estimated curvature and the determined relative position, an own vehicle lane probability instantaneous value for each object ahead is repeatedly determined. An own vehicle lane probability is determined by performing a filter calculation on the calculated own vehicle lane probability instantaneous value. Based on the determined own vehicle lane probability, a preceding vehicle is selected. Characteristics of the filter calculation are set such that an object ahead associated with a preceding vehicle selected in a previous processing cycle is relatively less affected by the own vehicle lane probability instantaneous value than an object ahead associated with an object other than the preceding vehicle.