The quadrupole and octupole polarizabilities for the ground states of lithiumlike systems from Z=3 to 20 are calculated with the full-core plus correlation method. For the neutral lithium atom, the typical patterns of convergence of the quadrupole and octupole polarizabilities are analyzed. The calculated quadrupole and octupole polarizabilities of the ground state for lithium atom are compared with the previous theoretical results obtained by other methods; our predictions agree with the most accurate reports in the literature very well. For lithiumlike ions, our prediction may provide valuable reference data for other accurate theoretical calculations in future. (C) 2004 American Institute of Physics.