Fabry-Perot-based ultrasound sensors at fiber tips have performed high sensitivity and immunity of electromagnetic interference with a relatively compact size. Nevertheless, the reverberation at fiber tips causes a strong noise that degrades the sensing capability. Here we propose a fiber optical-based ultrasound sensor with three design approaches to reduce the reverberation, including designs with an eccentric core, absorptive shield, and arc edge. The effect was experimentally validated with a photoacoustic signal excitation. Compared with bare single-mode fibers in simulation, the low-reverberation design increased the signal-to-noise ratio by 32.1 dB with identical excitation. The experimental results demonstrated the "clean" response with almost invisible reverberations, which was validated by a commercial hydrophone. This research solved the reverberation problems and provided a low-noise design for fiber optic ultrasound sensing.