Hybrid structures based on graphene and carbon nanotubes (CNTs) are one of the most relevant modern nanomaterials for applications in various fields, including electronics. The variety of topological architectures of graphene/CNT hybrids requires a preliminary study of their physical properties by in silico methods. This paper is devoted to the study of the electronic and electrical properties of graphene/CNT hybrid 2D structures with an island topology using the self-consistent charge density functional-based tight-binding (SCC-DFTB) formalism and the Landauer–Buttiker formalism. The island-type topology is understood as the atomic configuration of a graphene/CNT hybrid film, in which the structural fragments of graphene and nanotubes form “islands” (regions of the atomic structure) with an increased density of carbon atoms. The island-type graphene/CNT hybrid structures are formed by AB-stacked bilayer graphene and (6,3)/(12,8) chiral single-walled carbon nanotubes (SWCNT). The bilayer graphene is located above the nanotube perpendicular to its axis. Based on the binding energy calculations, it is found that the atomistic models of the studied graphene/SWCNT hybrid structures are thermodynamically stable. The peculiarities of the band structure of graphene/SWCNT (6,3) and graphene/SWCNT (12,8) hybrid structures are analyzed. It is shown that the electronic properties of graphene/SWCNT hybrid structures are sensitive to the orientation and size of the graphene layers with respect to the nanotube surface. It is found that an energy gap of ~0.1 eV opens in the band structure of only the graphene/SWCNT (6,3) hybrid structure, in which the graphene layers of the same length are arranged horizontally above the nanotube surface. We revealed the electrical conductivity anisotropy for all considered atomistic models of the graphene/SWCNT (12,8) hybrid structure when bilayer graphene sheets with different sizes along the zigzag and armchair directions are located at an angle with respect to the nanotube surface. The obtained knowledge is important to evaluate the prospects for the potential application of the considered atomic configurations of graphene/SWCNT hybrid structures with island-type topology as connecting conductors and electrodes in electronic devices.