A vehicle driving assist apparatus includes an first calculator to calculate a degree of acceleration suppression, a controller to suppress target acceleration based on the degree of acceleration suppression, a map information storage to store road map information, an estimator to estimate a vehicle position and identify a traveling lane on the road map information, a detector to detect whether there is a crossing road ahead of the identified traveling lane, and a second calculator to calculate an azimuth angle difference between an azimuth of the crossing road where the own vehicle is about to turn and an azimuth in the traveling direction of the own vehicle. The acceleration suppression degree calculator makes a degree of acceleration suppression for suppressing the acceleration of the own vehicle higher then an azimuth angle difference becomes narrower based on the azimuth angle difference.