The dipole polarizabilities of the lithium-like ground states, 1s22s 2S, are calculated with the full-core plus correlation (FCPC) wavefunctions. The non-relativistic polarizabilities are obtained by using a variation-perturbation method. Based on the relativistic and QED corrections to the energy, the dipole polarizabilities are corrected using an oscillator strength formula. The results indicate that relativistic and QED effects on the dipole polarizability become very important for Z>or=15. The result for Li I, 164.08 a03, is in good agreement with a recent CI-Hylleraas calculation, 164.1 a03 and with the experiment, 164.0+or-3.4 a03. The calculated results of other lithium-like systems are compared with previous theoretical results in the literature.