The present invention discloses a permanent magnet synchronous motor system with a LC filter and a method capable of realizing position-sensor-less control by using the permanent magnet synchronous motor system. The PMSM system comprises a current acquisition module, a Clark transformation module, an extended state observer(ESO) module, an angle and speed calculator module, a counter-electromotive-force calculation module, a microcontroller unit(MCU), a three-phase inverter, the LC filter and a permanent magnet synchronous motor. The present invention provides a sensor-less extended state observer method used for the permanent magnet synchronous motor. According to the method, the angle and the speed of the permanent magnet synchronous motor equipped with the LC filter are estimated without using position sensor(s), so that the sensor-less control is realized; and without changing system hardware(s), the problem of the sensor-less control of the permanent magnet synchronous motor withthe LC filter is solved by using the extended state observer.