A sheet medium stacking conveying device and method, wherein the method comprises a medium conveying step, the medium conveying step comprises: moving a stacking mechanism for clamping media from a medium inlet to a medium outlet along a moving path, and discharging the media clamped by the stacking mechanism towards the medium outlet relative to the stacking mechanism in a process of moving the stacking mechanism towards the medium outlet. The stacking mechanism of the conveying device can reciprocally move between a collection position and discharge position of the media under the driving of a driving mechanism, and the media can be discharged under the condition of no additional power source.