To provide a method and a device to control the running speed of an automobile so as to prevent the occurrence of a risky state, taking in to consideration that a driver can be dazzled by the light of an opposite vehicle.

At least one inter-vehicle distance to a front running vehicle or other obstacle is decided (S41) by an inter-vehicle distance sensor and the actual running speed of a vehicle to be controlled is decided (S42). When it is decided by a dazzle sensor (S44) that the driver of a vehicle to be controlled is dazzled by the light of an opposite vehicle, positive acceleration of the vehicle to be controlled is not effected or the actual running speed of a vehicle to be controlled is reduced at S46.