A gear drive system includes a securing panel, a first slave gear, a drive gear, and an adjusting structure. The securing panel includes a panel body, a rack, and a rotating shaft. An upper part of the first slave gear is adjacent to the rack and aligned with the rack. The drive gear engages the first slave gear. The adjusting structure includes an elastic element, a slave element pivotally mounted to the panel body, and a third slave gear. The third slave gear defines a rotating hole. The rotating shaft is received in the rotating hole. The second slave gear is movable related to the panel body to enable the rotating shaft to be located in different positions of the rotating hole. The third slave gear is driven to move and rotate. The slave element is driven to rotate to press the elastic element.