Density Functional Theory (DFT) calculation of the type (B3LYP) and 6-311G basis set level using Gaussian-03 program were carried out for equilibrium geometry of construction units of (6,0) linear ZigZag SWCNT (mono, Di, Tri and Tetra ring layers), to evaluate the geometrical structure (bond length), symmetries, physical properties and energetic such as standard heat of formation (ΔH0f), total energy (Etot.), dipole moment (μ), Highest Occupied Molecular Orbital Energy (EHOMO), Lowest Unoccupied Molecular Orbital Energy (ELUMO), energy gap (ΔEHOMO-LUMO), the distribution of electron density () and vibration frequencies, all at their equilibrium geometries. Assignment of the vibration frequencies according to the group theory was done applying the Gauss View program. Comparison were done for the distribution of electron density, vibration frequencies with the studying the relationship of all the physical and electronic properties for ZigZag SWCNTs with its construction units.