Terahertz (THz) absorber with dynamically tunable bandwidth possesses huge application value in the field of switches, sensors and THz detection. However, the perfect absorbers based on traditional metamaterials are not intelligent enough to capture the electromagnetic wave in a tunable way. We utilized monolayer graphene and cross-shaped metallic sub-wavelength structure to design broadband absorber with tunable absorption frequency in terahertz regime. The absorption frequency can be turned by changing the chemical potential of graphene which can be easily controlled by the bias voltage supplied to graphene. Simulation results show that 1.3 THz average bandwidth was achieved. And the almost perfect absorption shifted from 2.04 THz~3.53 THz to 3.15 THz~4.24 THz continuously.