A high-resolution fiber sensor system based on fiber Bragg grating (FBG) laser is proposed and demonstrated. The fiber laser sensor is made by writing Bragg grating into a section of high gain active fiber. Unmeasured singals applied on the fiber laser induce laser frequency shifts. And a polarization-insensitive unbalanced Michelson fiber interferometer is employed to transpose the frequency shifts into phase shifts of the interferometer. After converting the output singals of the interferometer to electric signals, the signals are sampled and input into the computer. An improved normalized phase generated carrier (PGC) demodulation technique is used to achieve high resolution demodulation. Experiments demonstrate that the dynamic stain resolution of this system is 5.6×10-4 nε/Hz, and the system output is linear to the strain of the fiber laser sensor.