A mobile object control apparatus, with respect to a first mobile object and a second mobile object, predicts whether the first and second mobile objects will collide with each other at an intersection. The apparatus calculates, when the first and second mobile objects will collide with each other at the intersection, a speed of the first mobile object at which the collision can be avoided at the intersection. The processor extracts a third mobile object that is in an intersection area and has passed through the intersection, and estimates that the third mobile object has a high possibility of colliding with the first mobile object at the intersection. The intersection area is set at the intersection through which the first mobile object passes.