The electromagnetic characteristics of the permanent magnet linear generator (PMLG), which is the key components of the free-piston engine (FPE), are studied in this paper. First of all, the velocity, displacement, and output voltage of the flat-type linear generator used in the experimental platform in the half-motion cycle are simulated by the model of 3D electromagnetic field and verified by experiment, and the relation curves of the output voltage to running velocity are found. Then, the PMLG is re-designed as a tubular type with two different structures of the permanent magnet on the steel backing of the mover: rectangular and the I-shaped. Third, the new PMLGs are modeled, and the models are used to do a simulation to investigate the influence of the structure of permanent magnet on the electromagnetic characteristics under no-load and load conditions. It is found that the fundamental wave amplitude of the flux density in the air gap of Ishaped PMLG is 0.93 T, greater than the rectangular one (0.87 T), and the proportion of the fundamental wave is higher. The waveform of the no-load induced electromotive force of the I-shaped PMLG is much better than that of the rectangular one, and the voltage total harmonic distortion (VTHD) is only 3.05%. The detent force analysis shows that the permanent magnet shape has a great influence on the detent force, and the peak value of detent force between I-shaped and rectangular PMLGs is significantly decreased from 25.4 to 7.75N. Moreover, the relation of the generator output power-velocity and efficiency-velocity under different loads is found. When the load is constant, with the velocity increases, the difference of output power between the I-shaped and rectangular structures becomes bigger. The optimum range of running velocity of the generator with the higher efficiency under different loads is presented. In conclusion, the I-shaped structure of the permanent magnet is a better choice for FPE.INDEX TERMS Free-piston engine, optimum range of running velocity, permanent magnet linear generator, structures of permanent magnet structure, voltage total harmonic distortion.