In this paper, a polarization-insensitive and dual-band Electromagnetic Induced Transparency-Like (EIT-Like) metamaterial is proposed, which is made of a cross-shaped graphene structure. Due to the mutual coupling between intralayer and interlayer, two high transmission windows can be obtained in different frequency bands. The sensibilities located at the two transmission peaks are calculated as 0.385 THz/RIU and 0.979 THz/RIU, respectively. In addition, the maximum group index of 174.5 is obtained. By adjusting the Fermi level of graphene, the transmission and group index could be modulated independently. The characteristics make the proposed metamaterials possess the potential as a tool for biological detection, slow light technology, and filters in THz region.

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