Disclosed is a vane compressor in which cylinders concentrically formed at the side of a rotor are eccentrically inserted in ring-shaped spaces between cylindrical parts concentrically formed at the side of a stator. A pair of radially extending vane attachment grooves is formed in the rotor, and vanes are slidably attached in the vane attachment grooves. Compression chambers the volumes of which repeatedly increase and decrease with each rotation of the rotor are concentrically formed in multiple stages by the cylindrical parts of the stator, the cylinders of the rotor, and comb-tooth parts of the vanes. It is possible to realize a vane compressor in which compression chambers can be concentrically arranged in multiple stages in a simple structure by suppressing increase in the number of components to the minimum level.