A horizontal moving & rocking appliance and chair includes a ground piece, mid and rear rollers eccentrically positioned at a mid and rear ends of ground pieces, synchronous link rods hinged between mid and rear rollers. In stationary state, the mid roller positioning shaft is in a forward rolling lower position while the rear roller positioning shaft is in a backward rolling higher position, and these together with the fore ends of ground pieces form a three-ground point; A horizontal moving & rocking chair includes a chair and horizontal moving & rocking appliance mounted on both sides of legs.