A construction machine, in particular a road milling machine, comprising a machine frame, a traveling mechanism with front and rear traveling devices with at least one pair of front traveling devices and/or one pair of rear traveling devices, at least one pair of the front or rear traveling devices being connected to the machine frame via lifting columns each having a hydraulically adjustable piston-cylinder unit, a drive device for driving the hydraulically adjustable piston-cylinder unit of the lifting columns separately from one another, and a control device configured to control the lifting adjustment of the lifting columns by means of the hydraulically adjustable piston-cylinder units, and to a method for controlling the lifting position of a piston-cylinder unit of a lifting column of a construction machine, in particular a construction machine according to the invention.