A maximum permissible acceleration is calculated so as to take into account vehicle stability, driver's comfort, road surface information and traffic information, driver's specific taste in acceleration and deceleration, and the like. An acceleration limiting process is carried out, in which a feedback gain in vehicle speed feedback control is corrected as may be necessary based on a relationship between the maximum permissible acceleration and actual acceleration information so as to keep the actual acceleration within the maximum permissible acceleration. The present invention thereby makes it possible to control a vehicle speed within a desired acceleration range even under conditions, in which there is a large vehicle speed deviation as in a resume mode, causing an excessively large acceleration or deceleration to tend to occur. Auto cruise control offering an outstanding safety and comfort can thus be implemented.