A driving assist apparatus of a vehicle of the invention sets a predicted route predicted for the vehicle to move and performs an attention operation to a driver when a time predicted for the vehicle to reach a point where a moving object crosses the predicted route is smaller than or equal to a threshold time. The apparatus predicts a radius of a route predicted for the vehicle to move as a left turn radius when the vehicle turns left and sets a route curved along an arc having the left turn radius as the predicted route. The apparatus predicts the radius of the route predicted for the vehicle to move as a right turn radius when the vehicle turns right and sets the route curved along the arc having the right turn radius as the predicted route.