A self-propelled construction machine, having a milling drum housing having a sealing device which has a sealing element arranged in the working direction of the construction machine behind the milling drum, an adjustment device for adjusting the height position of the sealing element, and a controller for controlling the adjustment device of the sealing element. The sealing device has a scraper element, which is pivotably arranged on the sealing element such that the scraper element rests on the milled material and is pivoted in relation to the milling drum on the basis of the height of the milled material. The height position of the sealing element is adjusted on the basis of the pivot position of the scraper element.