The vehicle running control apparatus (driving support ECU 10) determines whether or not the driver of the vehicle is in an abnormal state in which the driver has lost an ability to drive the vehicle, and stops the vehicle by reducing the vehicle speed to 0 after an abnormality determination time point when the driver is determined to be in the abnormal state. The vehicle running control apparatus predicts a position at which the vehicle stops when the vehicle speed is reduced at a predetermined deceleration, when the predicted stop position is not within a stop prohibited area (for example, a curved road and a section within a predetermined distance from a point at which the road changes from the curved road to the straight road), it decelerates the vehicle with the deceleration and stops the vehicle. In contrast, the vehicle running control apparatus makes the vehicle ran with a constant speed when the predicted stop position is within the stop prohibited area.