A media stacking apparatus for an automatic media dispenser, comprising: a media box provided with a seating space, said media box allowing media to be pulled and stacked in said seating space via an inlet opening; feeding means provided in proximity of said inlet opening, said feeding means being provided to face each other and to rotate in opposite directions relative to one another so that the media are pulled into the seating space via said inlet opening; a guiding means being positioned to face the inlet opening and absorbing an impact exerted on a leading end of a medium pulled into the media box by the feeding means and pressing down the medium after the medium collides against the guiding means, wherein the guiding means comprises a damping unit colliding against the leading end of the medium conveyed by the feeding means; and the media stacking apparatus further comprises a pressing unit rotating in cooperation with the damping unit to press down a trailing end of the medium; and an elastic member provided between a rear surface of the damping unit and the media box to exert a restitution force on the damping unit when the medium collides against the damping unit, characterized in that the damping unit is hinged to one surface of the media box; and the damping unit comprises: a collision plate formed of a plate having a small thickness and inclined downward to face a supporting plate for the medium, said supporting plate being provided on a bottom surface of the seating space, whereby said collision plate is configured to collide against the leading end of the medium; and a rotating plate having a width relatively smaller than that of the collision plate and rotating together with the collision plate when the leading end of the medium collides against the collision plate; wherein the pressing unit is connected to the rotating plate via a link. a media box provided with a seating space, said media box allowing media to be pulled and stacked in said seating space via an inlet opening; feeding means provided in proximity of said inlet opening, said feeding means being provided to face each other and to rotate in opposite directions relative to one another so that the media are pulled into the seating space via said inlet opening; a guiding means being positioned to face the inlet opening and absorbing an impact exerted on a leading end of a medium pulled into the media box by the feeding means and pressing down the medium after the medium collides against the guiding means, wherein the guiding means comprises a damping unit colliding against the leading end of the medium conveyed by the feeding means; and the media stacking apparatus further comprises a pressing unit rotating in cooperation with the damping unit to press down a trailing end of the medium; and an elastic member provided between a rear surface of the damping unit and the media box to exert a restitution force on the damping unit when the medium collides against the damping unit, characterized in that the damping unit is hinged to one surface of the media box; and the damping unit comprises: a collision plate formed of a plate having a small thickness and inclined downward to face a supporting plate for the medium, said supporting plate being provided on a bottom surface of the seating space, whereby said collision plate is configured to collide against the leading end of the medium; and a rotating plate having a width relatively smaller than that of the collision plate and rotating together with the collision plate when the leading end of the medium collides against the collision plate; wherein the pressing unit is connected to the rotating plate via a link.