A medium transporting apparatus is used for transporting a label web including a carrier web and labels adhered thereto. A platen roller transports the label web in a transport path. A pressure roller is disposed downstream of the separating member with respect to the transport path, and causes the carrier web to be kinked. The pressure roller urges the carrier web against the platen roller. A support member is mounted on a cover and rotatably supports the pressure roller. The cover is pivoted between an open position and a closed. Immediately after the cover has moved to the closed position, the pressure roller contacts the platen roller and then slides by a predetermined amount on the circumferential surface of the platen roller in a direction away from the separating member. Thus, the carrier web sandwiched between the pressure and platen rollers becomes taut.