Graphene‐based absorbers have various modern applications across industries due to their exceptional properties. Some common applications include: thermal management and energy storage. Herein, the design and simulation of a broadband tunable absorber based on graphene with perfect absorption spectra in the near‐infrared region are reported. The proposed structure consists of an MgF2 layer and golden disc surrounded by L‐shaped golden arms placed on single layer of graphene. The structure guarantees polarization‐insensitive (PI) performance under normal incident due to the symmetrical design. The investigation of the PI of the structure reveals almost similar absorption for oblique incident angles up to 55° for TM and up to 60° for TE polarization. The desirable resonance wavelength is achievable by tuning the geometrical parameters. By changing the chemical potential of graphene, the absorption and bandwidth of absorber are controllable. A full width at half maximum of 330 nm is another superiority of this absorber. These considerable aspects of the proposed structure make it practical for varieties of applications such as cloaking, sensing, switching, and so on.