The creation of tunable Fano resonances in a photonic crystal structure with a side-coupled nanocavity and a waveguide with a partially transmitting element is investigated in this paper. In the proposed structure, the nanocavity’s central hole is made up of two cylinders with different radii that are nested inside each other. The outer and inner cylinders are made of quartz and liquid crystal, respectively. The performance of this device is analyzed using the three-dimensional finite-difference time-domain. The transmission spectrum, resonance wavelength, and quality factor of the proposed structure are calculated for various applied voltages. It is demonstrated that as the applied voltage increases, the quality factor changes and the Fano resonance wavelength shifts. Based on the findings, a tuning range of 5.2 nm is achievable with an excellent transmission contrast within this range. The presented structure is appropriate for applications such as tunable switches and filters.