The invention discloses a self-stabilizing three-stage air-distribution low-NOx pulverized coal burner. A pre-burning chamber and a conical barrel formed by the cone expansion and extension of an internal secondary air duct are arranged in an external secondary bellows. A large end of the conical barrel is sheathed in an external secondary air passage formed by an opening at one end of the pre-burning chamber. A wall surface at the other end of the pre-burning chamber, which is closed with an external end face of the external secondary bellows, is provided with an annular tertiary air passage.A central air duct is coaxially arranged in a primary air duct. The primary air duct and a cone expanding end of the central air duct are both arranged in the conical barrel. The internal secondary air duct sheaths the outside of the primary air duct. An axial movable cyclone impeller is arranged in the internal secondary air duct. The outer end of the axial movable cyclone impeller is provided with an internal secondary air impeller pull rod. An annular passage of a separating plate is provided with an air regulator. The outer end of the air regulator is provided with an air regulating pullrod. The circumference at the inner end of the air regulating pull rod is equally divided to arrange sliding fins cooperating with an internal secondary bellows in a sliding manner. The burner has strong self-stabilization capability, can adjust a flame position, prevent slag formation in the pre-burning chamber and realize low NOx emission, and is capable of wide application in various industrialpulverized coal boilers.