Considering that nanoindentation size effect under very small nano scale could not be effectively investigated by traditional experimental methods, this paper proposed to use quasi-continuum (QC) method to establish a multi-scale simulation model for nanoindentation process on single crystal copper at very small depth, below 20Å. And different-size small indenters were adopted in this paper with their radiuses ranging from 2nm to 10nm. The simulation results showed that the contact stiffness did not show indentation size effect, but the values fluctuated on a horizontal line; that the nano-hardness showed obvious indentation size effect.