In the Nd-Fe-B permanent magnet materials, existing of small amount of copper can increases the coercivity which is very important property of the magnet. In order to understand the microscopic mechanism of the effect of copper on the properties of the Nd-Fe-B magnet, first-principles calculations based on density functional theory coupled with cluster expansion method are performed to investigate the phase stability in Cu-doped Nd and Nd-O system. Calculations revealed that Cu is stable in both NdO-ZnS and N2O3-cI80 structures in a wide oxygen concentration range and the possible existing state of Cu in Nd-rich phase might be a solid solution of (Nd,Cu)O-ZnS.