The combination of photonic crystal fiber (PCF) and graphene-supporting surface plasmon polaritons (SPP) presents a new approach to achieving a plasmonic sensor with adjustable properties in the terahertz (THz) frequency range. In this study, we investigate a liquid-core PCF-based graphene plasmonic sensor, where the analyte to be detected is located on both the sensing layer surface and the fiber core. As a result, the dispersion relations of both graphene plasmon (GP) and core-guide mode can be influenced by the analyte, leading to a negative refractive index (RI) wavelength sensitivity. This unique performance is attributed to the higher modulation degree of the core mode on the analyte RI (Δneff.core) compared to that of the GP mode (Δneff.GP). By reducing the graphene Fermi energy, a positive sensibility is achieved with the modulation relationship of Δneff.core < Δneff.GP. Subsequently, the geometry dependence is explored to optimize the sensing capabilities. Furthermore, we demonstrate the sensor’s tunability by dynamically varying the graphene Fermi energy (Ef). By adjusting the Ef from 0.6 to 0.9 eV, the detection range can be artificially shifted from 0.554–0.574 THz to 0.686–0.724 THz, obtaining a tunability of 0.44 THz/eV and a higher sensitivity of 1.2667 THz/RIU. This design facilitates the efficient utilization of the limited bandwidth to detect various RIs and provides a flexible approach to constructing multiple sensing channels. To the best of our knowledge, this is the first report of graphene plasmonic sensing based on core-filled PCF in the THz frequency range. The novel analysis method of modulation degree and dispersion matching has the potential to be widely applied in THz plasmonic sensing and could lead to various nanoscience applications.