A theoretical study on Cu2n±(n=0,1,2) using density functional method (B3LYP/LANL2DZ) shows that Cu2, Cu+2,Cu-2,Cu2-2 are stable . Electronic ground states are 1Σg＋（Cu2），2Σg（Cu＋2），2Σu（Cu-2）and 1Σg（Cu22-）and their force constants and spectroscopic data have been worked out .The potential energy curves of Cu-2 and Cu2-2 have both minimum and maximum, which are the so-called“energy trapped”molecules，while Cu2+2 is unstable. At the same time, the effect of charge on the potential energy function and energy levels for Cu2n±(n=0,1,2) are discussed.