In this paper, a tunable graphenebased broadband tunable microwave absorber is proposed, which is composed of a gridtypegraphene structure, a dielectric layer and a metal floor. The performance of the device is simulated by CST software. The simulation results show that when the Fermi level of graphene is 0.5 eV, the electromagnetic wave absorption rate of the device is 90% in the frequency range of 2.97~3.74 THz. On the other hand, the operating frequency of the device can be dynamically adjusted by changing the Fermi level of graphene. When the Fermi level of grapheneis changed from 0.3 eV to 0.8 eV, the operating frequency of the device can be tuned in the frequency range of 2.60~4.55 THz and the relative tuning bandwidth is 56%. And in the entire tuning frequency range, the electromagnetic waveabsorption rate of the device is always higher than 90%. In addition, the performance of the device is insensitive to the polarization direction and incident angle of the incident electromagnetic wave, so the device has potential applications in the fields of terahertz imaging, terahertz detection and stealth technology.