The free-piston generators have the advantages of simple structure, high power density and high efficiency, so they are proposed for applying in the series hybrid electric vehicles (HEV). In this paper, a novel PM linear magnetic-geared machine serving as the free-piston generator is proposed. The machine consists of a linear permanent magnet synchronous machine (PMSM) and a linear magnetic gear (LMG), which are integrated together. The proposed machine adopts a structure that the high-speed mover of the LMG and the translator of the linear PMSM share the same moving part. There are four main parts in the machine topology, including the low-speed mover with PMs, the ferromagnetic pole pieces, the high-speed mover with PMs and the stator with three-phase windings. In order to improve the speed of the PMSM translator, the magnetic-geared topology is adopted, such that the designed machine can generate the high-voltage electricity and have the high power density. In the magnetic-geared machine, the tubular stator is designed as a 12-slot structure with concentrated windings. In order to integrate the machine and the magnetic gear magnetically and mechanically together, the high-speed mover of the magnetic gear is designed as the translator of the machine. The tubular machine translator consists of one row of PMs. And the low-speed mover of the magnetic gear consists of a tubular iron core and PMs mounted on the inner face of the core. The PMs of both low-speed mover and machine translator are radial magnetized. Between the low-speed mover and the high-speed mover of the magnetic gear, the ferromagnetic pole pieces are fixed there to modulate the magnetic fields. Since the LMG has the advantage of high force density inherently, the proposed novel PM linear magnetic-geared machine can obtain the high power density, high efficiency and weight reduction by comparing with the conventional linear machines. This work is performed and verified by using the finite element analysis (FEA) method.