The non-relativistic energy and wave function of high angular momentum 1s2ng (5 = n = 8) states of lithium-like isoelectronic sequence from ScXIX to ZnXXVIII are calculated using the full-core-plus-correlation (FCPC) method. Relativistic effects and mass polarization effects are considered as perturbations, and their corrections to system energy are estimated. In order to get hold of high-precision theoretical results, it is also necessary to consider the contribution of quantum electrodynamics (QED). Based on the single-channel quantum defect theory, the quantum defects of 1s2ng Rydberg series are determined, and the results are in full compliance with its physical laws. Comparing the ionization potential obtained by the semi-empirical method with the FCPC method, it can be seen that the results are in good agreement. Consequently, the ionization potential can be extrapolated to the energy territory with larger principal quantum numbers to forecast the approximate value of unknown energy levels, which provides theoretical instruction for relevant studies.