The possible geometrical and electronic structures of fullerene C20 tetramer are optimized by using the density functional theory (b3lyp) at the 6-31G level. For the ground state structures of C20 tetramer, the stability properties, natural bond orbits (NBO), the spectrum, the polarizability and the aromatic characteristics are analyzed. The calculated results show: C20 tetramer may be synthesized by [2+2] addition reaction of C20 carbon cages, which have good thermal stability. Carbon atoms in C20 tetramer are in sp2 hybridization and these atoms happen to have charge transfer. There are a lot of vibration peaks in IR and Raman spectra of C20 tetramer. The bonding interactions between atoms of C20 polymer increase with increasing number of the carbon cages. The C20 tetramer has aromaticity.