We propose a model of hole transport along a DNA double helix. In this model, DNA molecule is described as a quasi-one-dimensional double-stranded system containing two chains base pairs connected by hydrogen-bonded bridges. We study the processes of dynamical screening of the mobile holes by the charge on the H-bond bridges. We show that a such screening strongly acts the insulator/conductor behavior in both DNA-strands which can have important consequences for the hole conductivity.