A vehicle speed control system for controlling the speed of a controlled vehicle to follow a preceding vehicle detected at a constant interval is provided. In this system, when a preceding vehicle traveling ahead of the controlled vehicle is detected, it is checked if the preceding vehicle detected meets a given tracking condition. When the tracking condition is encountered, it is reported to a driver. The system is responsive to a manual operation of the driver after the driver has perceived that the preceding vehicle can be tracked to initiate constant inter-vehicle distance control.