Terahertz (THz) absorber with dynamically tunable bandwidth possesses huge application value in the fields of switches, sensors, and THz detection. However, the perfect absorbers based on photonic crystals and metamaterials are not intelligent enough to capture the electromagnetic wave in a tunable way. In this paper, we utilized only patterned graphene to tune the absorption positions and the bandwidth in the terahertz regime. More distinguished than some dynamic absorbers proposed before, the performances with peak frequency relative tuning range of 68 % and nearly unity absorbance are obtained by a single cross-shaped graphene layer. Additionally, the working bandwidth can be broadened with stacked structured graphene. The almost perfect absorption shifted from 2.36 similar to 3.2 to 3.26 similar to 3.99 THz continuously via changing the chemical potential of graphene.