A novel topology of aircore permanent magnet linear synchronous motor (PMLSM) which has an asymmetrical doubleside trapezoidal permanent magnet (PM) stator was proposed in this paper. Firstly, a 3D magnetic field analytical model of one trapezoidal PM was established based on the theory of magnetic charge, and a 3D model of the flux distribution in the airgap of a doubleside PMLSM could be obtained by the superposition principle. Expressions of the back electromotive force and the electromagnetic force are derived with considering the transverse end effect of the coil. The analytical model was used for evaluating and optimizing the distribution of airgap flux density harmonics. Subsequently, the proposed model was verified by a 3D finite element analytical model to demonstrate its accuracy.