It is preferred to insert a saturable absorber grating in Er-doped fiber ring lasers for obtaining a stable single-longitudinal-mode laser operation; however, mode hopping is hardly avoided in various applications. A new mode hopping mechanism is found by utilizing the interferometric phase-demodulation method to transfer the optical frequency hops to the phase changes in real time. The regular mode hops triggered by fast cavity-length modulation are measured, and the characteristics and the origin of the mode hopping are obtained. Experimental results show that this kind of mode hopping, usually occurring between two neighboring longitudinal modes, may appear near the maximum slope of the modulation curve, and the laser frequency with shift about the space of the longitudinal modes before mode hopping. In addition, both the threshold frequency of the optical frequency modulation and the minimal frequency shift, which can triggered a mode hop, increase with the pump power at the same modulation amplitude. These experimental results can provide the stable operation condition if vibration or modulation exists, and they are helpful for optimal designing of the isolated assemblage or determining the operation range under the modulation condition.