A sheet pressing apparatus assembled to a file processing equipment which has an input tray for stacking sheets and a pickup roller for feeding sheets. The sheet pressing apparatus includes a sheet pressing assembly movably mounted to the file processing equipment, a driving device including a connecting member and a stepping motor, a sensor unit and a control system. The sheet pressing assembly is driven by the stepping motor to be descending through the connecting member. When the sheet pressing assembly descends, the sensor unit touches the sheets and sends a signal to the control system, the control system figures out the thickness of the sheets by calculating steps the stepping motor having passed, then the control system makes the stepping motor further move with certain steps to drive the sheet pressing assembly further descend to apply a suitable pressure on the sheets.