We constructed a tunable Fabry-Perot interferometer (FPI) by controlling the effective refractive index of pitch-variable subwavelength gratings (PV-SWGs) that were incorporated into an FP cavity. The period of the PV-SWG can be varied to change the effective refractive index and shift the optical resonant frequency of the FPI. Compared with conventional methods that tune the optical resonance by adding fillers or deforming the cavity, the proposed FPI obtained a higher transmission and quality factor (Q-factor) for the transmittance peak, and its resonant frequency can be shifted by simply stretching the PV-SWG. A peak transmittance of 0.87, a Q-factor of 34, and a frequency shift of 17 GHz were obtained by the PV-SWG-based FPI for THz incomes around the frequency of 0.303 THz. As the effective refractive index and the working frequency can be tailored by altering the geometry design of the PV-SWG, the FPI holds significance for the development of THz communications and for applications at different wave bands.