A driving assist apparatus of a vehicle of the invention predicts, as a predicted minimum left turn radius, a curvature radius of a moving route of the vehicle at a point where a curvature radius of the moving route is predicted to become smallest when the vehicle turns left, and sets a route curved along an arc having the predicted minimum left turn radius as a predicted moving route predicted for the vehicle to move. The apparatus predicts, as a predetermined minimum right turn radius, the curvature radius of the moving route of the vehicle at the point where the curvature radius is predicted to become smallest when the vehicle turns right, and sets the route curved along the arc having the predicted minimum right turn radius as the predicted moving route.