To obtain a variable speed driving system for permanent magnet synchronous motor in which an overvoltage is prevented from being applied to an input smoothing capacitor upon missing a DC power supply voltage and a small lightweight system is realized inexpensively by eliminating an AC circuit switch.

In a method for driving a permanent magnet synchronous motor 7 through an inverter 600 connected with a DC power supply 1, the motor 7 is driven until the peak value of no-load induced voltage of the motor exceeds the voltage of the DC power supply. Open circuit of the DC circuit between the DC power supply and the inverter 600 is detected by a detection circuit 630 and if the DC circuit is opened when the r.p.m. of the motor exceeds a specified value, the inverter 600 controls the synchronous motor 7 such that the torque current component thereof goes zero.