A vehicle speed control system for a vehicle comprises a lateral acceleration sensor, a vehicle speed sensor, a target vehicle speed setting device, a drive system of the vehicle, and a controller connected. The controller is arranged to calculate a correction quantity on the basis of the lateral acceleration and the vehicle speed, to calculate a command vehicle speed on the basis of the vehicle speed, the target vehicle speed, a variation of the command vehicle speed and the correction quantity, and to control the drive system to bring the vehicle speed closer to the command vehicles speed.