The invention discloses a single-groove unipolar cylindrical moving-magnet linear alternating-current generator. The single-groove unipolar cylindrical moving-magnet linear alternating-current generator comprises a stator assembly and a rotor assembly, wherein the stator assembly and the rotor assembly are coaxial, the stator assembly comprises an iron yoke and a coil body, the coil body is wound in a coil duct of the iron yoke, the rotor assembly comprises an inner iron yoke, four permanent magnets and permanent magnet spacer rings, the four permanent magnets are coaxial with the inner iron yoke and are tightly attached to the inner iron yoke, the four permanent magnets are spaced from one another through the permanent magnet spacer rings, the polarities of the two permanent magnets on one side are the same and are opposite to the polarities of the two permanent magnets in the middle, generator air gaps are formed between a pole shoe of the iron yoke and the four permanent magnets, and the rotor assembly moves in the stator assembly in a reciprocating mode. According to the single-groove unipolar cylindrical moving-magnet linear alternating-current generator, the sizes of the generator air gaps are small, the air gap flux density is high, and the generator can be directly coupled with an engine making reciprocating motion or a heat engine making reciprocating motion. The single-groove unipolar cylindrical moving-magnet linear alternating-current generator has the advantages of being high in power density, high in efficiency, simple in structure, convenient to machine and manufacture and the like and can serve as an thermoelectric conversion device for Stirling heat engines consuming solar energy, nuclear thermal energy and biomass energy and other heat engines making linear motion for output.