To easily cover a coolant piping connecting an indoor unit to an outdoor unit of an air conditioner by forming a strip-like covering body which covers an outside of the air conditioner piping from fibers, and arranging engagement means which engage with each other on both sides of longitudinal direction of the strip-like covering body.

Hook-like engagement means 9a, 9b which are engaged with each other are arranged on both sides of a longitudinal direction of a strip-like covering body 8 with proper spacings in the longitudinal direction. A heat insulator material 5 outside indoor or outdoor two pipngs 4 are bundled together with an electric wire and covered by means of the covering body 8 from outside. The covering body 8 is laid along the longitudinal direction of the bundle. The bundle is then covered with the covering body 8. The engagement means 9a, 9b on both sides are engaged with each other. The covering body 8 is thus attached to the bundle. The coolant piping 4 connecting an indoor unit of an air conditioner to an outdoor unit can easily be covered.