A permanent magnet electrical rotating machine having a permanent magnet rotor and a stator, wherein:a plurality of permanent magnets are disposed in a rotor iron core of the permanent magnet rotor along a periphery of the rotor iron core, polarities thereof being alternately changed;a cooling airflow channel is formed between each pair of adjacent opposite poles on the rotor iron core; and the cooling airflow channel has an approximately trapezoidal shape on an outer periphery side of the rotor iron core; and extends from an end on a central side in a radial direction of the approximately trapezoidal shape to a radial center.