A travel assist apparatus performs assist of warning or auxiliary for preventing departure of a vehicle in a lateral direction of the vehicle. A value of the estimated time to lane crossing at which assist is to be performed is varied in accordance with the velocity of the vehicle in the lateral direction. This enables selection of a value of the estimated time to lane crossing at which assist is to be performed that is suitable for the velocity of the vehicle in the lateral direction, enabling optimization of the timing of performing assist. Therefore, assist of warning or auxiliary is performed in an optimal way without bothering the driver.