The present invention relates to a leek peeling machine, consisting of a functional assembly, preceded by a feeder which individually introduces the leeks, comprising a thrusting system (B) to transport the leeks towards the inside of the machine, a cutting system (C) which produces longitudinal cuts in the outer layer of the leeks, a peeling system (D) which removes the outer layer of the leeks, and an extracting system (E) which draws the clean leeks towards the outside of the machine.