The Vernier effect has been widely used in the field of measurement and instrumentation for sensitivity enhancement. Single-point optical fiber sensors based on the Vernier effect have been extensively reported in recent years. In this Letter, for the first time, a distributed optical fiber sensor based on microwave photonics with improved sensitivity enabled by the Vernier effect is demonstrated. Distributed sensing is realized by interrogating a Fabry-Perot interferometer (FPI) array formed by cascaded reflectors along an optical fiber using an optical carrier-based microwave interferometry (OCMI) system. A reference FPI is also included in the system. The interferogram of each of the sensing FPIs can be unambiguously reconstructed and superimposed with the reconstructed interferogram of the reference FPI to generate the Vernier effect. By tracking the spectral shift of the envelope signals in the superimposed spectra, the measurement sensitivities of the sensing FPIs can be significantly improved. A simple direct modulation-based OCMI system is used in the proof-of-concept demonstration, showing sensitivity-enhanced distributed sensing capability. Moreover, the sensitivity amplification factor can be adjusted by varying the optical length difference of the sensing and reference FPIs, similar to that of Vernier effect-based single-point optical fiber sensors.