Neutral lithium has a relatively simple three-electronic structure and thus accurate theoretical calculations including quantum electrodynamics (QED), isotope shift, and relativistic corrections can be obtained from many-body wave functions. The development of high precision spectroscopy of lithium offers a benchmark to such theories and can be used to determine the nuclear radius and measure the fine structure constant, thus testing fundamental physical laws with higher accuracy.We report the precision measurement of the absolute frequencies, hyperfine splitting, and 2P fine structure splitting in cold atoms of 6Li. Using the stabilized optical frequency comb and developed heterodyne detection technique, the photon shot-noise limited optical spectroscopy is achieved. The measurement of absolute frequencies of D1 lines is reached with an uncertainty of about 1 kHz. Our results could provide a benchmark to test the theory at the higher precision and help to resolve large discrepancies among previous experiments.