This study presents a dynamic strain sensor system based on the fiber ring laser containing a semiconductor optical amplifier. In this sensing system, the semiconductor optical amplifier based fiber ring laser in combination with a fiber Bragg grating is used as a wavelength selecting component of the fiber laser to detect the external dynamic strain signal. A non-tunable fiber Fabry-Pérot filter is deployed outside the laser cavity as an intensity demodulator, and the function of separating and outputting the reflected signals of multiple fiber gratings can be realized by configuring the fiber bandpass filter. Experimental results show that the proposed sensing system has a good response to the dynamic strain signal at a frequency of up to 200 kHz, and it has the ability to demodulate the MHz frequency range signal. The feasibility of multiplex demodulation is also verified. The system has a simple structure and low cost, and can be applied to the detection of dynamic strain signals in structural health monitoring.