In sensorless control of a permanent magnet synchronous motor (PMSM), the initial position estimation is difficult. An accurate estimation method based on square-wave voltage injection with frequency conversion and double phase-locked loop is proposed. First, the polarity of the rotor is determined by applying a low frequency square wave voltage in the opposite direction of the same amplitude. Then, the frequency is increased to 3 kHz, and a double phase-locked loop is used to compensate the rotor position adaptively to improve estimation accuracy. Finally, it keeps signal injection for PMSM start-up with no-load and load experiments. The injected signal is not interrupted nor changed during the whole process. Experiments show that the maximum error is less than 3.73°, and the average estimate time is 0.18 s. The motor remains stationary. When the PMSM is started up, the double phase-locked loop shortens the time by 18 ms compared with the PLL and the maximum compensation angle is 38.39°. The estimation process does not introduce sensitive parameters, and the system has good stability and speed. This work is supported by the National Natural Science Foundation of China (No. 51707195).