The electronic properties of diamond surface are easily affected by its surface covered layer, like species, concentration and structure of the surface covered layer. At present, the surface covered layer with stable configuration and excellent performance is still under study. In our work, transition metal (Cu) is used as the surface covered layer. The transition metal (Cu) studied in this paper is not only widely used in semiconductor micro-fabrication, but also has excellent performance of heat dissipation, which is very similar with diamond on this point. Moreover, ultrathin layer of Cu has recently been deposited on diamond as an epitaxy, where the thermally stable and characteristic of negative electron affinity were found. As a result, Cu-covered diamonds have become more important than ordinary electrodes, and it is very important for the Cu-diamond structure to modify and tailor electronic properties of diamond (001) surface. In this paper, the adsorption energy, stable configuration and energy band structure of diamond (001) surface covered by transition metal (Cu) with different coverage (0.25 ML， 0.5 ML and 1 ML) have been studied by density functional simulation. The results show that Cu as a surface coating can induce a negative electron affinity about -0.5 eV to -0.3 eV and a Schottky barrier height(ΦBH) of -0.16 eV to 0.04 eV, which is in good agreement with the experimental data. At the same time, the diamond (001) surface covered by the transition metal (Cu) with various coverage has also shown the stable configurations. Therefore, all these results suggest that Cu as a surface coating have an important application in diamond-based electron emission device.