The electronic states and electrical transport properties of the Cu doped wurrite type ZnO were investigated by the plane wave ultro-soft seudo-potentials based on the density functional theory calculations. The calculational results show that the Cu doped wurrite type ZnO has approximately 0.6 eV direct band gap and it is p type semiconductor, there are newly formed bands within the valence bands and conducting bands that are from the electons of dopant Cu. The bands near Fermi level are formed by the Cu p, Cu d as well as the O p state electrons and there are high interactions between them. The analyzing results of the electrical transport properties show that carriers within the valence bands have heavy effective mass and the carriers within the conduction bands have light effective mass for the Cu doped wurrite type ZnO. The carrier transport process is estimated to be accomplished by the Cu p, Cu d as well as the O p state electrons. Furthermore, the energy gap for electron or hole carriers to surpass is narrowed by Cu doping for Zn.