A seat sliding apparatus for a vehicle includes lower rails, upper rails, screw mechanisms provided between the upper rails and the lower rails, the screw mechanism including a screw shaft and a nut which is engaged with the screw shaft, one of the screw shaft and the nut being mounted to the upper rail so as to rotate, the other of the screw shaft and the nut being fixedly mounted to the lower rail, and a slide driving mechanism including a driving motor, a transmission mechanism for transmitting a rotational force outputted from the driving motor to one of the screw shaft and the nut so as to rotate, a bracket having the driving motor and the transmission mechanism mounted thereon and connecting the upper rails, and a protection cover attached to the bracket for covering at least lower and bottom sides of the driving motor and the transmission mechanism.