In this paper, we present an ultra-compact 1D photonic crystal (PhC) Bragg grating design on a thin film lithium niobate slot waveguide (SWG) via 2D- and 3D-FDTD simulations. 2D-FDTD simulations are employed to tune the photonic bandgap (PBG) size, PBG center, cavity resonance wavelength, and the whole size of PhC. 3D-FDTD simulations are carried out to model the real structure by varying different geometrical parameters such as SWG height and PhC size. A moderate resonance quality factor Q of about 300 is achieved with a PhC size of only 0.5μm×0.7μm×6μm. The proposed slot Bragg grating structure is then exploited as an electric field (E-field) sensor. The sensitivity is analyzed by 3D-FDTD simulations with a minimum detectable E-field as small as 23mV/m. The possible fabrication process of the proposed structure is also discussed. The compact size of the proposed slot Bragg grating structure may have applications in on-chip E-field sensing, optical filtering, etc.