On a stator core (3), there are wound primary generating windings (W U ,W V ,W W ) of four (4) poles with a distributed full-pitch winding structure and stator excitation windings (W e ) with a concentrated full-pitch winding structure, having the number of poles odd-number times the number of poles of the primary generating windings, that is, twelve (12) poles. The primary windings appropriately produce spatial higher harmonic components of the armature reaction magnetic fields. The excitation windings are connected to the center taps (u,v,w) of the primary windings through a control rectifier (5). On a rotor core (7), six field windings (W f1 - W f6 ) of four poles. The field windings are arranged at positions where they are magnetically coupled with both static magnetic fields produced by the stator excitation windings and odd-order spatial higher harmonic components of armature reaction magnetic fields produced by the currents (I₁,I₂,I₃) in the primary generating windings. The field windings are short-circuited by the diodes (D₁,D₂,D₃,D₄,D₅,D₆), respectively. In the brushless self-excited synchronous generator, the number of slots in each of the rotor and stator can be determined irrespective of the order number of the spatial higher harmonic components of the armature reaction magnetic fields. The generator is simple and rigid in its structure.