Surface plasmon resonance has found plenty of sensing applications on various platforms from label-free biosensing to surface-enhanced spectroscopies. Quasiperiodic nanohole arrays with patterns such as the Penrose tiling have been demonstrated with surface plasmon resonance enhanced optical transmission. Here we transfer quasiperiodic nanohole arrays onto optical fibers and measure their optical performance in refractive index sensing. These quasiperiodic arrays show multiple and narrow resonances related to their geometric features. These resonances are high sensitive to the dielectric changes on the probe surface due to our high quality fabrication. The sensitivity of quasiperiodic nanohole arrays is comparable to that of periodic nanohole arrays and reaches the theoretical sensitivity limit as predicted by our universal sensitivity analysis. This result verifies our sensitivity theory on propagating surface plasmon resonance in a wider range beyond periodic nanostructure arrays. Our study demonstrates the quasiperiodic nanohole array based optical fiber is a high-performance plasmonic sensor.