In this research paper, we introduce a band-stop filter based on an hourglass-shaped graphene nanoribbon topology. Employing the three-dimensional finite difference time domain (3D-FDTD) method, we conduct comprehensive numerical simulations to investigate transmission spectra and electromagnetic field distributions. Our primary objectives are to achieve high transmission efficiency, increase tunability, and ensure compact dimensions. The hourglass-shaped band-stop filter exhibits a remarkable bandwidth of 1.2 THz, a 90 % transmission efficiency in the passband, an impressive attenuation of −52.5 dB at the resonance frequency of 32.3 THz, and a compact footprint of 400×300 nm2. By manipulating the chemical potential (or bias voltage) to control the conductivity and dielectric constant of the graphene surface, we set the center frequency of the filter in the range of 28 to 36 terahertz. The remarkable combination of high transmission efficiency, high tunability, and compact design makes our proposed filter an ideal candidate for integration.