A vehicle driving control apparatus is provided for controlling an own vehicle to track a target vehicle. The vehicle driving control apparatus includes: (1) means for acquiring an actual relative speed of the target vehicle to the own vehicle; (2) means for setting a target acceleration of the own vehicle based on the product of a relative speed gain and the actual relative speed acquired by the acquiring means, the relative speed gain being normally set to a reference gain; (3) means for detecting occurrence of an event which causes the target acceleration set by the setting means to discontinuously change; and (4) means for correcting, upon detection of occurrence of the event by the detecting means, the relative speed gain so as to gradually increase the relative speed gain from a value that is less than the reference gain.