A crystal plasticity finite element method (CPFEM) model has been developed to investigate the indentation size effect (ISE) of aluminium single crystal during nano-indentation. The simulated results have been validated by comparison with experimental observations. The load-hardness curves from simulation are consistent with the experimental results. The mathematic relationship between load and indentation depth has been built to investigate indentation size effect. In addition, the Mises stress, critical resolved shear stress, stress and shear strain rates for a selected element and the lattice curvature have been studied to explain indentation size effect.