The mouse factor Zif268, known also as early growth response protein EGR-1, is a classical representative for the Cys2His2 transcription factor family. It is required for binding the RNA polymerase with operator dsDNA to initialize the transcription process. We have shown that only in this family of total six Zn-finger protein families the Zn complex plays a significant role in the protein-DNA binding. Electrostatic feature of this complex in the binding of factor Zif268 from Mus musculus with operator DNA has been considered. The factor consists of three similar Zn-finger units which bind with triplets of coding DNA. Essential contacts of the factor with the DNA phosphates are formed by three conservative His residues, one in each finger. We describe here the results of calculations of the electrostatic potentials for the Zn-Cys2His2 complex, Zn-finger unit 1, and the whole transcription factor. The potential of Zif268 has a positive area on the factor surface, and it corresponds exactly to the binding sites of each of Zn-finger units. The main part of these areas is determined by conservative His residues, which form contacts with the DNA phosphate groups. Our result shows that the electrostatic positive potential of this histidine residue is enhanced due to the Zn complex. The other contacts of the Zn-finger with DNA are related to nucleotide bases, and they are responsible for the sequence-specific binding with DNA. This result may be extended to all other members of the Cys2His2 transcription factor family.