The extended LEPS of O-2-Cu single crystal plane systems is constructed by means of 5-MP (the 5-parameter Morse potential). Both the adsorption and dissociation of O-2 on Cu low-index surfaces are investigated with extended LEPS in detail. All critical characteristics of the system that we obtain, such as adsorption geometry, binding energy, eigenvalues for vibration, etc., are in good agreement with the experimental results. Our calculated results suggest there are many differences between O-2-Cu (110) and O-2-Pd (110) systems. On a Cu (110) surface, O-2 adsorbs in a tilted configuration and there are two lowest energy dissociation channels along the [001] and [110] directions, respectively. We speculate that the adsorption geometry of O-2 on the metal surfaces relates to the lattice constant of metal. Meanwhile, We use the concepts of the molecular dissociation limit and the surface dissociation distance to analyze again the dissociation mechanism of the O-2 on the low-index surfaces.