A vehicular driving assist system includes a sensor disposed at a vehicle and sensing forward of the equipped vehicle. With the equipped vehicle traveling along a traffic lane of a road, the system, responsive to processing of sensor data captured by the sensor, determines a leading vehicle traveling along the traffic lane ahead of the equipped vehicle. The system determines position and heading information of the leading vehicle relative to the equipped vehicle. As the equipped vehicle approaches locations that correspond with the determined position and heading information of the leading vehicle, the system adapts the position and heading information of the leading vehicle to the current location and heading of the equipped vehicle and controls lateral movement of the equipped vehicle to follow the leading vehicle in and long the traffic lane of the road.