The structure and electronic properties for five two-dimensional (2D) C-36 slabs with a C-36 per unit cell and the supergraphite structure with two C-36 per unit cell are calculated using ab initio self-consistent field crystal orbital method based on B3LYP density functional theory. The calculations show that the structure stabilities are dependent on steric hindrance and size of aromatic domains. All the models are semiconductors. The band structures of corresponding anionic C-36(m-) (m = 1-4) slabs with a C-36 per unit cell are also calculated. It is found that the extra electrons fill the unoccupied bands of neutral crystals almost in a rigid-band manner. The superconducting possibility in those metallic slabs is discussed on the basis of the electron-phonon coupling mechanism. It seems that the 2D C-36 slabs with a C-36 cage per unit cell cannot produce a superconducting transition temperature much higher than those in alkali metal-doped C-60 crystals.