Illite is a common clay mineral that is found in a wide range of geological settings. The good thermal stability and non-swelling properties of illite make it valuable in ceramic materials, paints and coatings, drilling fluids, agriculture and geological studies. To gain a deeper understanding of the physical and chemical properties of illite, in the present paper the atomic and electronic structures of a typical trans-vacant 1M Al-rich illite were constructed and calculated using density functional theory. The calculated indirect band gap of Al-rich illite was 4.99 eV. The electronic analysis revealed that the interactions in the tetrahedral sheet were more stable than those in the octahedral sheet. The substitution of Al atoms noticeably reduced the stability of the tetrahedral sheet in Al-rich illite. Other properties of Al-rich illite, including the density of states, electron population/charge, electronic charge density and bonding interaction, are also discussed and analysed in detail.