The goal of this paper is to propose a novel concept of permanent magnet machine with integrated airfoil-shaped rotor that can perform compression action. Electrically driven conventional compressor systems need electric machines as prime movers to provide mechanical energy to rotate the compressor. The proposed novel integrated permanent magnet machine system synthesizes both an electric machine and an axial-flow compressor into a single device to convert electrical power to mechanical rotational power of the rotor, which simultaneously compresses the gas. This novel integrated design simplifies the compressor system by eliminating the connection between the electric machine and compressor. Weight, volume, and cost savings are expected. The feasibility of the proposed concept is demonstrated by combining the principle knowledge in electric machine design and compressor design. The operating principles of this novel integrated machine are described in the paper. Analytical design methods are used to study the proposed integrated machine and compressor. Possible topology variations of the proposed concept are discussed.