A novel fiber sensor for curvature and acoustic wave measurement, which is based on a thin core ultralong period fiber grating (TC-ULPFG), has been proposed and experimentally demonstrated. By tracking the power variation of different resonant wavelength caused by TC-ULPFG, high curvature sensitivity of 97.77 dB/m–1 is achieved, to best of our knowledge, which is the highest than other structures at the same measurement range. Thus, the desired curvature property of the TC-ULPFG is used for acoustic measurement. The polyethylene terephthalate film is selected as a transducer, on which TC-ULPFG is tightly pasted. The acoustic pressure sensitivity of 1.89 V/Pa is two orders higher than other structures based on the diaphragm transducer, and the noise-limited minimum detectable pressure is 1.94 mPa/Hz1/2 at 200 Hz. In addition, the frequency fluctuations are nearly ±0.4 dB from 70 to 200 Hz and ±0.2 dB from 1 to 3 kHz. Therefore, the proposed optical fiber acoustic sensor has a flat frequency response at a relatively lower frequency. The TC-ULPFG shows many advantages, including high sensitivities of curvature, high acoustic pressure sensitivity, easy fabrication, simple structure, and low cost.