A suction apparatus, a glass-wiping device and a run control method thereof. The suction apparatus comprises a suction cup unit (1). The suction cup unit (1) comprises an inner suction cup (11) and an outer suction cup (12). The inner suction cup (11) is arranged on the inside of the outer suction cup (12). A chamber on the inside of the inner suction cup (11) forms an inner negative pressure chamber (13) via vacuum suction. A chamber between the inner and outer suction cups (11 and 12) forms an outer negative pressure chamber (14) via vacuum suction. The outer negative pressure chamber (14) is connected to a vacuum detection unit. The vacuum detection unit comprises a distensible piece (20) and a distension-sensing piece (21). The distensible piece (20) is sealedly connected onto an opening on the top end of the outer negative pressure chamber (14). The distensible piece (20) has arranged thereon the distension-sensing piece (21). The glass-wiping device is provided with the suction apparatus, when in cases of failure of the outer suction cup (12) in the suction apparatus and of failure of the outer negative pressure chamber (14), the glass-wiping device will take measures immediately to prevent an increased number of small protrusions from entering the inner suction cup (11), thus preventing the phenomenon of the glass-wiping device falling off a wall from occurrence.