The electronic ground state and the electric conductivity of W-type hexagonal ferrite BaFe18O27 are investigated in the generalized gradient approximation (GGA) as well as the GGA plus Hubbard U(GGA+U) scheme. The ionic relaxation calculation of the experimental crystal structure shows that oxygen ions at 6h site in the BaO layer move away from the surface position in the unit cell, resulting in a structural distortion. The magnetic moment of the cell is calculated to be 28 B/f.u., in agreement with previous experimental results. By taking account of electronic band structure and crystal ionic configuration it is found that the material is a weak half-metal and the effective mass of conduction electrons along the c axis is much heavier than that perpendicular to this axis. Fe ions on octahedral 6 g sites and O ions around them of the spinel block form a conductive layer. Therefore the electric conductivity perpendicular to the c axis is much greater than that parallel to the c axis.