In the paper, the full-core plus correlation (FCPC) and the minimizing the expectation value of the Hamiltonian method is extended to calculate the non-relativistic energies and the wave functions of 1s22s states for the lithium-like systems from Z=21 to 30. The mass-polarization and the relativistic correction included the kinetic-energy correction, the Darwin term, the electron-electron contact term, and the orbit-orbit interaction are calculated perturbatively as first-order correction. The contribution from quantum electrodynamic (QED) is also included by using the effective nuclear charge formula. The ionization potential and term energies of the ground states 1s22s are given and compared with other's theoretical calculation and experimental results. It is shown that the FCPC methods are also effective to theoretical calculation of the ionic structure for high nuclear ion of lithium-like systems.