Abstract Graphene, a new smart material, has attracted remarkable attention in recent years owing to its tunable band structure and strong light–matter interaction. Compared to typical absorber, graphene absorber is recently considered as a highly promising candidate for multi-mode purpose. Here, a new tunable hexagonal-shape graphene-based THz absorber is proposed. To achieve nearly perfect broadband terahertz absorption, six layers of graphene is utilized. By introducing such a unique gradient, the continuous plasmon resonances of the absorber can be directly excited and broadband terahertz absorption can be achieved. Additionally, contrary to conventional absorbers which often neglect the high-order modes, particularly in THz regime, the proposed absorber has the advantage of achieving unit absorbance peak not only for the first resonance mode, but for higher order modes. To validate the sensitivity of the proposed absorber, frequency sensitivity and amplitude sensitivity are calculated. The highest frequency sensitivity is achieved 15.3012 for the second mode at θ = 60 ∘ and the highest amplitude sensitivity is estimated to be 45.1482 for the fourth mode at the same incident angle.