A vehicle speed control apparatus is provided. In particular, a storage configured to store a table (hereinafter, referred to an area table) recording an area corresponding to a speed of a vehicle and a condition of a road; an imaging device configured to take a front image of the vehicle; an image processor configured to calculate an area of a shape made by a driving lane of the vehicle and a preceding vehicle in the driving lane from the front image of the vehicle taken by the imaging device; a road information collector configured to collect condition information of the road; and a controller configured to set a speed corresponding to the condition information collected by the road information collector and the area calculated by the image processor as a driving speed of the vehicle, based on the area table.