This paper presents the analysis and optimization of air-core permanent magnet linear synchronous motor with overlapping concentrated windings to achieve high thrust density, high thrust per copper losses and low thrust ripple. For the motor design, we adopt equivalent magnetizing current (EMC) method to analyze the magnetic field and give analytical formulae for calculation of motor parameters such as no-load back EMF, dynamic force, thrust density and thrust per copper losses. Further, we proposed a multi-objective optimization by genetic algorithm to search for the optimum parameters. The design optimization is verified by 2-D Finite Element analysis (FEA).