Photo-ionization cross sections for the ground and the n ≤ 5 excited states of lithium atoms are calculated in the photoelectron energy ranging from threshold to 0.5 Rydberg. The wavefunctions for both the bound and continuum states are obtained by solving the Schr(o)dinger equation numerically in a symplectic scheme.Our results are in excellent agreement with the recent experimental measurements and in harmony with other theoretical calculations.