Vehicle travelling control device and method

A vehicle traveling control device includes a sensor for detecting a steering operation, an object information acquisition device for acquiring object information around a vehicle, an automatic braking device for automatically braking the vehicle, and a driving support ECU for controlling the automatic braking device, in which the driving support ECU activates the automatic braking device to perform automatic braking for automatically braking the vehicle in a case where it is determined based on the object information acquired by the object information acquisition device that there is a risk of off-road departure of the vehicle and also it is determined based on the steering operation detected by a sensor that a steering operation has been performed in a direction of the off-road departure of the vehicle.