This paper has developed electromagnetic equations based an analytical model to design a three-phase line start permanent magnet synchronous motor (LSPMSM) of 2.2 kW. In order to enhance the torque and efficiency of this machine, an optimized slot shape of rotor permanent magnet is proposed. The analytical model is first presented to evaluate the magnetic characteristics, and then analytical expressions are derived under the open circuit condition. The influence of the magnet size variables on the analytical model is considered to investigate the magnetic leakage flux and flux density distribution in air gaps. Moreover, the variation of design has a significant impact on the steady-state performance characteristics of this motor. In addition, in order to check the output results from the analytical model, a finite element method is developed to evaluate these solutions. Finally, experimental and simulation results have been compared and analyzed to validate the development of method.