A vehicle speed control device performs vehicle speed control for controlling the vehicle speed of a host vehicle so that the vehicle speed of the host vehicle becomes a preset vehicle speed that is set in advance when a preceding vehicle traveling ahead of the host vehicle is not detected and for controlling the vehicle speed of the host vehicle so that the host vehicle follows the preceding vehicle when the preceding vehicle is detected. The vehicle speed control device determines whether the host vehicle is positioned in an acceleration-control-inhibited area based on the position detected by a position detection unit and, when the preceding vehicle is not detected and a position determination unit determines that the host vehicle is positioned in the acceleration-control-inhibited area, the vehicle speed control device performs acceleration-control-inhibition vehicle speed control of the host vehicle.