An apparatus for detecting a vehicle running in a blind spot detects, with a predetermined accuracy, a first target position of a target which is present in a first detection area that extends obliquely rearward of the vehicle, detects, with an accuracy lower than the predetermined accuracy, a second target position related to a target which is present in a second detection area adjacent to the first detection area; calculates a first estimated position that corresponds to a subsequent position of the target that has been detected by the detection section as the first target position; and adopts the first estimated position as a position of the target when the first estimated position is included in a predetermined range centering on the second target position, adopts the second target position as a position of the target when the first estimated position is outside the predetermined range.