Generally, transverse magnetic (TM) polarization-based surface plasmons (SPs) are excited in plasmonic devices. While the transverse electric (TE) modes can be excited in graphene up to the visible frequency range, TM modes can be supported only from terahertz to the mid-infrared region. We show that graphene TM modes can be excited in the visible spectrum by applying a suitable voltage to the graphene layer and using an appropriate interfacing dielectric layer thickness. Furthermore, utilizing this TM mode, we propose a dual-channel refractive index sensor where the same analyte can be injected into the two channels for significantly sensitive detection of the analyte, or two different analytes can be injected into the two channels for their simultaneous detection. The proposed sensor exploits two graphene layers, one with nanostrip arrays, for efficient TM mode excitation. The nanostrips in the first graphene layer scatter the incoming radiation to the second, generating TM modes at both layers. The proposed dual-channel sensor shows 2530 degrees/RIU peak sensitivity when the sensing channels have the same analyte. The graphene nanostrips-based sensor will be a promising alternative to the traditional Kretschmann arrangement and significantly impact biosensing and refractive index sensing without needing noble metal in the structure.