This paper describes the analysis and design optimization of an improved axially magnetized tubular permanent-magnet machine. Compared with a conventional axially magnetized tubular machine, it has a higher specific force capability and requires less permanent-magnet material. The magnetic field distribution is established analytically in the cylindrical coordinate system, and the results are validated by finite-element analyses. The analytical field solution allows the analytical prediction of the thrust force and back-electromotive force (emf) in closed forms, which, in turn, facilitates the characterization of a machine, and provides a basis for design optimization and system dynamic modeling.