A dispenser and system for dispensing sheet material is provided. The dispenser includes a housing including a container and a lid. The container and lid cooperate to provide an inner surface formed to include an internal compartment configured to hold sheet material. The housing includes an exit port for withdrawal of sheet material therefrom. The dispenser also includes a sheet mover mounted to the housing. A portion of the sheet mover is configured to move over at least a portion of a sheet material positioned in the housing such that at least the portion of the sheet material is moved away from additional sheet materials positioned adjacent thereto by the sheet mover. The portion moved away is positioned to be easily withdrawn through the exit port by a user. The system includes the dispenser having a sheet mover and a plurality of sheet materials disposed in the dispenser. A disposable, one-use dispensing system is provided as well.