This preceding-vehicle determination apparatus comprises: a vehicle speed sensor which detects the speed of a host vehicle; a preceding vehicle detection sensor which detects the position of a preceding vehicle ahead of the host vehicle; a steering angle sensor which detects the steering angle of the host vehicle; a low speed determination section which determines whether or not the vehicle speedof the host vehicle detected by the vehicle speed sensor is at a determination threshold value or less; a radius of curvature estimation section which estimates the radius of curvature R of the road on which the host vehicle is travelling on the basis of the steering angle if the vehicle speed is equal to or less than the determination threshold value; a coordinate conversion section which converts, on the basis of the radius of curvature R, the position of the preceding vehicle in a first coordinate system in which the curve corresponding to the radius of curvature R is used as the reference,to the position in a second coordinate system in which the straight line along the straight traveling direction of the host vehicle is used as the reference; and a host vehicle lane probability calculation section which calculates, on the basis of the position of the preceding vehicle in the second coordinate system, a probability that the preceding vehicle is present in the lane on which the host vehicle is travelling.