A new variation method is extended to study the atomic systems with higher nuclear charges and in more highly excited states. The non-relativistic energies of 1s2np (n ≤ 9) states for the lithium-like systems from Z=11 to 20 are calculated using a full-core-plus-correlation method with multi-configuration interaction wavefunctions. Relativistic and mass-polarization effects on the energy are calculated as the first-order perturbation corrections. The fine structures are determined from the expectation values of spin-orbit and spin-other-orbit interaction operators in the Pauli-Breit approximation. The quantum-electrodynamics correction is also included. Our results are compared with experimental data in the literature.