Plasma treatment of gases in large volumes, treatment of powder materials and liquid under atmospheric pressure represent a significant issue because of specific properties of plasma sources. For decontamination of gases, there is used a creeping rotary discharge of the gliding arc type generated by a high-voltage source connected to a ground electrode with rotation symmetrical discharge chamber, and to an inner conical electrode arranged separately and rotatably inside the discharge chamber. The discharge is blown out of the discharge chamber by a stream of working transport gas. Disadvantage of the above consists in significant demands to a gas volume and a device output, as well as in a pressure difference deteriorating treatment process and limiting capacity and device efficiency. The present invention is based on generating a creeping rotary discharge of the gliding arc type without gas blowing out, but only by rotation of the inner electrode having a specific form of a discharge worm or a discharge propeller, without any negative pressure difference. The method of and apparatus according to the present invention are suitable for plasma treatment of gases, liquids, powder materials as well as solid materials.