A vehicle driving assist apparatus includes a first unit to set a degree of acceleration suppression to suppress acceleration of a vehicle, a controller to suppress target acceleration of the own vehicle based on the degree of acceleration suppression, a storage to store road map information, an estimator to estimate a vehicle position, a detector to map-match the estimated vehicle position to the road map information and detect whether there is a crossing road ahead of the vehicle, a second setting unit to set, when the detector detects the crossing road, a traveling-prohibited region on an opposite side of the vehicle on the road map information, and a calculator to calculate a reaching distance from the vehicle to the region. The degree of acceleration suppression is set to a higher value as the reaching distance becomes shorter.