This paper presents an improved conformal mapping (ICM) method for magnetic field analysis in one typical surface-mounted permanent-magnet(SMPM) motor considering the static, dynamic, and mixed rotor eccentricities. The ICM method accurately accounts for the slotting effect, the winding distribution, the armature reaction, the magnetic saturation effect, and the working point variation of PMs throughout their volume. The ICM method is also very rigorous to separate the onload air gap field components. First, the slotless model of an eccentric SMPM motor is mapped to one concentric model using a new form of bilinear conformal mapping, and the field solution is then obtained through applying Hague's solution in the main canonical domain. Second, the slotted air gap magnetic field is obtained through the modulation of air gap magnetic field in the slotless physical domain using the complex relative air gap permeance. The ICM method is also used to investigate the influence of rotor eccentricity on the flux linkage of the stator coils. This developed model is validated through comparing with the corresponding results obtained through finite element method and the frozen permeability method. This method can also be used as a tool for design and optimization of electrical machines.