On the basis of the crystal structure model of BaCoxZn2-xFe16O27 , their ground electronic states and dielectric properties have been investigated using the generalized gradient approximation plus Hubbard U approach. The co-substitutions of cobalt and zinc cause the electrical conductivity of BaFe18O27 to change from a half-metallic to semiconductive. With the increase of Co content x, the energy gap of BaCoxZn2-xFe16O27 increases but the lattice constants and the magnetic moment of the unit cell decrease. The calculations of dielectric constants show that the static dielectric constants increase with x, lie in a range of 6.2-7.2 and appear to be anisotropic. Through the Born electric charge analysis it is shown that the polarization of Co and Zn itself has little effect on the polarization of the material and the main polarization may be related to the polarization of the iron and oxygen ions, caused by the crystal distortion.