A cruise control for a vehicle that detects an inter-vehicle distance to a preceding vehicle. A first vehicle speed instruction value is computed based on the inter-vehicle distance. Curve information of a curve in the road ahead of the vehicle is detected, and a second vehicle speed instruction value is computed for traveling on the curve based on the curve information. A final target vehicle speed is set based on the vehicle speed instruction values. When the vehicle travels through the curve while the first vehicle speed instruction value is larger than the second vehicle speed instruction value, the final target vehicle speed is set to a vehicle speed higher than the second vehicle speed instruction value and lower than the first vehicle speed instruction value. The speed of the vehicle is controlled based on the final target vehicle speed.