The non-relativistic energies of 1s2 ns (6 ≤ n ≤ 9) states for the lithium-like systems from Z = 11 to 20 are calculated by using a full-core-plus-correlation (FCPC) method. The relativistic and mass-polarization effects on the energy are calculated by the first-order perturbation corrections. The correction from the quantumelectrodynamics effect is also included using effective nuclear charge. Based on these results and the quantum defect theory, the quantum defects of 1s2ns series for these ions, as a function of energy, are determined. The comparisons between the ionization potentials for 1s2ns states (6 ≤ n ≤ 9) obtained by the FCPC method and the semi-empirical method are carried out. The results show that their agreement is very well and the energies of all discrete states (n ≥ 10) below the ionization threshold of this series for the ions can be predicted by using their quantum defects.