An air cleaning apparatus includes an air flow duct, with an extent in an axial direction, to accommodate air flow entering the apparatus, an air-conveying fan unit disposed in the air flow duct, a precipitator connected to a high-voltage source and with a throughflow passage for air to be cleaned. The precipitator includes two electrode elements or two groups of electrode elements, each of the respective two being connected to a respective pole of the high-voltage source, and a unipolar corona electrode disposed close to one end of the air flow duct. A target electrode is disposed at radial spacing from the corona electrode, the corona electrode being so disposed that the ions generated at it can freely spread away from the corona electrode towards the target electrode, and that the target electrode surrounds the air flow entering the apparatus.
