This paper proposes an optimal design method of permanent magnet machine (PMM) with cylindrical permanent magnet supported by magnetic bearings. The objectives of optimization design are minimizing the rotor loss while maximizing the power density of the PMM as well as the 1st order nature frequency of the rotor, and the constraints are size, the strength safety factor and the phase current. A 30kW, 48,000r/min PMM designed by the multi-objective optimization method is proposed and the results indicate: the rotor loss is decreased from 393W to 290W (is reduced by 26.2%); the power density of the PMM is increased from 1.86kW/kg to 2.19kW/kg (is increased by 17.7%); the 1st order nature frequency of the rotor is increased from 1579Hz to 1812Hz (is increased by 14.7%). The performances of the PMM are improved after optimization, which are verified by experiment.