A novel sensitivity enhanced fiber Bragg grating (FBG) strain sensor based on fine transmission spectrum and edge filter interrogator of a non-uniform FBG is proposed. The fine transmission spectrum changes of FBG under axial non-uniform strain and the strain response character based on spectrum changes are studied theoretically. The simulation results show that the strain sensitivity of the FBG under non-uniform strain can be enhanced to 4.6 times normal FBG. The sensor structure is designed and made experimentally to enhance the strain sensitivity by changing uniform strain into non-uniform strain. The experimental results are in good accordance with theoretical results. The FBG strain sensitivity and the range of the dynamic strain measurement ability are both enhanced in narrow linewidth laser locked edge filter interrogation system by using this new FBG sensor. Because of its compact size, the new FBG strain senor has great potential for high frequency dynamic strain monitoring.