By using the double-parameter perturbation method combined with a double-fold perturbation scheme, the energy levels for the low-lying excited states 1s2ns (n=3,4,5) of lithium-like atoms are calculated. The calculated results are in well agreement with experiment within a relative error of 0.8%. It is found that the electron can be regarded as moving in a circular orbit, corresponding to the assumption of steady state in Bohr theory. Moreover, it is shown that with the increase of the excited state of atom, the effective charge of inner electron remains largely the same, but the effective charge of the outer electron of the atom decreases. These findings would deepen our understanding of the electron related effects in atoms.