The fullcore plus correlation (FCPC) and the minimiziation of the expectation value of the Hamiltonian method is extended to calculate the nonreltivistic energies and the wave functions of 1s~2 nd(n=3,4,5) states for the lithium like systems from Z=11 to 20. The mass-polarization and the relativistic correction including the kinetic-energy correction, the Darwin term, the electron-electron contact term, and the orbitorbit interaction are calculated perturbatively as the first-order correction. The contribution from quantum electrodynamics (QED) is also included by using the effective nuclear charge formula. The excited energies, finestructure, and the termenergy are given and compared with other theoretical calculation and experimental results. It is shown that the correlative wave in the FCPC method embodies very well the strong correlation effect between the 1s~2 core and the valence electron.