Runaway electrons preionized diffuse discharge (REP DD) could generate volume non-thermal plasmas at atmospheric pressure, thus is widely used for surface modification. In this paper, two pulsed generators are used to produce REP DD for modifying copper (Cu) foil in atmospheric air. One generator produces repetitive pulses with a peak voltage of 40 kV and a rise time of 150 ns. The other generator produces single pulse with a peak voltage of 280 kV and a rise time of 0.5 ns. After the treatment, the modification results for including the macro topography, chemical composition and microhardness in different depths of the Cu surface are analyzed. In order to estimate the modification results in different areas of the Cu foil, several points from the center to the edge of the Cu sample are selected. It could be observed that the maximal modification effect usually appears in the area where the density of the diffuse discharge plasma is highest. The experimental results show REP DD treatment could significantly decrease the water contact angle and increase surface energy of the Cu foil. Meanwhile, it could decrease the carbon concentration and increase oxygen concentration in the near-surface layer of the Cu sample, and enhance the microhardness in different depths of the Cu foil.