In a vehicle braking assistance apparatus, a detection unit detects a target object in a traveling lane of an own vehicle. A braking assistance level determination unit, which determines a braking assistance level of the own vehicle by a braking device, determines, upon detecting a cut-in vehicle that has changed a travelling course to the travelling lane of the own vehicle using a detection signal from the detection unit, whether the cut-in vehicle is accelerable. The braking assistance level determination unit sets the braking assistance level of the braking to a high value that is higher than a standard value upon determining that the cut-in vehicle is not accelerable.