Permanent magnet synchronous machines have advantages such as small size, light weight, high efficiency, etc. It is more and more widely used in robots, electromagnetic propulsion, electric vehicles and so on. High power density and high torque density are urgent need for those applications. The electromagnetic design of machines mostly adopt multi-pole magnet patterns to reduce the stator yoke size. It helps to decrease the mass of the machine with the same power and improve the torque density. As the number of poles grows larger, the frequency and the core loss of per unit volume will also increase with the same speed, which can aggravate the heat problem of the machine. It is easy to generate the low-order vibration with high flux density. Therefore, the performance of a special-shaped external-rotor machine and comparisons with the traditional machine are analyzed in this paper. Numerical simulation is conduced to validated that the special-shaped magnet pattern can reduce the torque ripple, improve the torque output and power density. From the two-dimensional Fourier analysis of the radial electromagnetic force, it is found that the low-order amplitude of the special-shaped machine is greatly reduced, so the vibration can be avoided. Subsequently, the vibration simulation is carried out to indicate that the magnet pattern can satisfy low level in vibration and noise of the machine.