The present invention relates to a stair-climbing wheelchair (1) comprising a frame (2) provided with a seat (3) intended to accommodate a user (100) to be transported, a locomotion unit (4) comprising a couple of clusters of wheels (40). The wheelchair (1) comprises also passive supporting means movable between a stowed position wherein they are raised from the ground (la) and an extracted position wherein they are in contact with the ground (la). The passive supporting means comprise a track (6) configured in such a way that in said extracted position the frame (2) rests at the front on the locomotion unit (4) and at the rear on said track (6), the stair-climbing wheelchair (1) further comprises at least one mechanical device linked between the locomotion unit (4) and the seat (3) and adapted to cooperate with the track (6) for compensating the oscillations of the seat (3) generated by the movement of the couple of clusters of wheels (40), said at least one mechanical device being configured in such a way as to allow a translational motion of the seat (3) during a stair-climbing motion of the stair-climbing wheelchair (1).