The generalized gradient approximation based on density functional theory is used to analyze the structural and electronic properties of the unconventional exohedral fullerene C64Si. It is found that among four possible stable isomers, the structure with the single Si atom situated at the vertex of the directly fused pentagons, i.e., C64Si-1, is the most stable, which agrees well with the stable position of Si outside the C28 cage proposed by Ge et al. By analyzing the energy levels, orbital wave functions and density of states of both C64 and C64Si-1, Si atom is found to have greater contribution to the lowest unoccupied molecular orbital, but contribute less to the highest occupied molecular orbital. In addition, the effect of Si on the total density of states of C64 is very small. It is found from the vertical ionization potential and the vertical affinity that the ability for both detaching and obtaining electrons is decreased after the exohedral absorbing Si atom.