The gate-tunable absorption properties of graphene make it suitable for terahertz (THz) absorbers. However, the realization of a graphene-based THz absorber faces challenges between the difficulty of patterning graphene for processing and the intrinsically low absorbance of graphene with the high electric field needed to change the conductivity of graphene. This report presents an electrically tunable graphene THz absorber where a single-layer graphene film and a gold reflective layer are separated by a polyimide (PI) dielectric layer to form an easily fabricated three-layer Salisbury screen structure. The carrier density of the graphene layer can be efficiently tuned by a small external electrical gating (-5V-5 V) with the assistance of an ion gel layer. The voltage modulation of the Fermi energy level (EF) of graphene was confirmed by Raman spectra, and the variation of the device absorbance was confirmed using a THz time-domain spectroscopy system (THz-TDS). The measurements show that the EF is adjusted in the range of 0-0.5 eV, and THz absorbance is adjusted in the range of 60%-99%. The absorber performs well under different curvatures, and the peak absorbance is all over 95%. We conducted further analysis of the absorber absorbance by varying the thickness of the PI dielectric layer, aiming to examine the correlation between the resonant frequency of the absorber and the dielectric layer thickness. Our research findings indicate that the proposed absorber holds significant potential for application in diverse fields such as communication, medicine, and sensing.