An object detection apparatus is installed in a movable body and detects an object. The apparatus includes a first detection section which transmits search waves in a moving direction of the moving object, and receives reflected waves as detection information to detect the object, a second detection section which transmits search waves in the moving direction, and receives reflected waves as detection information, an obstacle determination section which determines that an obstacle is present in the moving direction, based on detection results of the first and second detection sections, and a crossing determination section which determines that the obstacle has crossed, in a state where the obstacle determination section determines that the obstacle is present, if the determination that the obstacle is present is made by continuous detection, and if a state where the object is continuously detected changes to a state where the object is not detected.