In order to measure the low-frequency vibration parameters of the structure， a thin-diameter Excessively Tilted Fiber Grating （ExTFG） cantilever vibration acceleration sensor is proposed， and the characteristics and optimization methods of the sensor are studied. Firstly， the characteristics of axial strain and bending strain of the thin-diameter ExTFG and the sensor model of vibration of cantilever beam are analyzed theoretically. Then， the influence of axial tension and bending strain on the vibration of the cantilever beam is analyzed by static experiments. Finally， the dynamic vibration test of cantilever beam is completed and compared with the standard-diameter ExTFG sensor. Experimental results indicate that under the effect of axial tension and bending stress， the axial strain sensitivity of TE and TM mode of the thin ExTFG is -4.68 pm/με and -3.55 pm/με， respectively， the wavelength based sensitivity of bending strain is -8.82 nm/m^-1 and -7.71 nm/m^-1， respectively， the intensity based sensitivity of bending strain is 6.71 dB/m^-1 and 0.95 dB/m^-1， respectively， and the thin ExTFG has a higher strain sensitivity than that of the standard ExTFG. In the cantilever vibration detection experiment， the maximum acceleration sensitivity at the 3 dB point is more than 500 mV/g， which is about 5 times of the standard-diameter ExTFG sensors under the same conditions. Compared with the spectral diagram after FFT transformation， the harmonic component of the thin-diameter ExTFG sensor is less than those of the standard one. Therefore， in the vibration sensing， the thin-diameter ExTFG has stronger anti-noise interference ability and higher detection accuracy.