We have proposed and implemented a novel scheme to obtain high-precision repetition rate stabilization for a polarization-maintaining mode-locked fiber laser. The essential technique lies in the periodic injection of electronically modulated optical pulses into a nonlinear amplifying loop mirror within the laser resonator. Thanks to the nonlinear cross-phase modulation effect, the injected pulses referenced to an external clock serves as a stable and precise timing trigger for an effective intensity modulator. Consequently, synchronous mode-locking can be initiated to output ultrafast pulses with a passively stabilized repetition rate. The capture range of the locking system reaches to a record of 1 mm, which enables a long-term stable operation over 15 hours without the need of temperature stabilization and vibration isolation. Meanwhile, the achieved standard deviation is as low as 100 μHz with a 1-s sample time, corresponding to a fluctuation instability of 5.0×10-12. Additionally, the repetition rate stabilization performance based on the passive synchronization has been systematically investigated by varying the average power, central wavelength and pulse duration of the optical injection.