Non-contact atomic force microscopy (NC-AFM) has been employed to observe double-stranded DNA. Cu(111) surface is found to be useful to realize high-resolution imaging of DNA molecules without the effect of water-layer and to improve the tip shape during the scan for imaging. NC-AFM images reveal the double-helix structure whose averaged repeat distance agrees with Watson-Crick model. However, the observed height of DNA molecules is only 1 nm that is the half of natural diameter of double-stranded DNA suggesting the strong deformation due to the surface adsorption. The simultaneous measurements of frequency-shift and tunneling current indicate that DNA molecules show tunneling conductivity across the strand with the attenuation factor β = 1.1.