This article reports a novel concept of computational microwave photonics and distributed Vernier effect for sensitivity enhancement in a distributed optical fiber sensor based on an optical carrier microwave interferometry (OCMI) system. The sensor system includes a Fabry-Perot interferometer (FPI) array formed by cascaded fiber in-line reflectors. Using OCMI interrogation, information on each of the interferometers (i.e., sensing interferometers) can be obtained, from which an array of reference interferometers can be constructed accordingly. By superimposing the interferograms of each sensing interferometer and its corresponding reference interferometer, distributed Vernier effect can be generated, so that the measurement sensitivity of each of the sensing interferometers can be amplified individually. This technique is achieved entirely in software without any physical modification to the system and negates the need to carefully fabricate the reference interferometer to obtain the desired magnification factor, as is often the case for traditional Vernier effect-based optical fiber sensors. Importantly, the reference interferometers can be flexibly constructed such that the magnification factor for each sensing interferometer can be precisely and easily controlled. The operating principle is illustrated in detail, followed by a proof of concept. The experimental results match well with theoretical predictions.