Lithium in the atmosphere of a F or G supergiant reflects the initial Li abundance and the internal history of the star . During evolution of a star from the main sequence ( MS ) to the supergiant phase , lithium may be destroyed by , for example , rotationally-induced mixing in the MS stars and strongly diluted by development of the supergiant ’ s convective envelope . In order to probe the connection between atmospheric Li abundance and evolutionary predictions , we present a non-LTE abundance analysis of the resonance doublet Li I at 6707.8 Å for 55 Galactic F and G supergiants and bright giants ( we observed 43 of them , the remaining 12 are added from Luck and Wepfer ’ s list ) . The derived lithium abundances \log \epsilon ( Li ) may be considered in three groups , namely : ( i ) ten Li-rich giants with \log \epsilon ( Li ) = 2.0 to 3.2 ( all ten are F-type or A9 stars ) ; ( ii ) thirteen G- to K0-type stars with Li abundances in the narrow range \log \epsilon ( Li ) = 1.1-1.8 ; ( iii ) all other stars provide just upper limits to the Li abundance . The derived Li abundances are compared with theoretical predictions of 2 to 15 M _ { \odot } stars ( both rotating and non-rotating ) . Our results are generally in good agreement with theory . In particular , the absence of detectable lithium for the majority of programme stars is explainable . The comparison suggests that the stars may be separated by mass M into two groups , namely M \lesssim 6 M _ { \odot } and M > 6 M _ { \odot } . All Li-rich giants and supergiants with \log \epsilon ( Li ) \geq 2.0 have masses M < 6 M _ { \odot } ; this conclusion follows not only from our work but also from a scrutiny of published data . Eleven of thirteen stars with \log \epsilon ( Li ) = 1.1-1.8 , specifically the stars with M < 6 M _ { \odot } , show good agreement with the post-first dredge-up surface abundance \log \epsilon ( Li ) \approx 1.4 predicted for the non-rotating 2-6 M _ { \odot } stellar models . An absence of Li-rich stars in the range M > 6 M _ { \odot } agrees with the theoretical prediction that F and G supergiants and giants with M > 6 M _ { \odot } can not show detectable lithium . We note that present theory appears unable to account for the derived Li abundances for some stars , namely for ( i ) a few relatively low-mass Li-rich giants ( M < 6 M _ { \odot } ) , whose high Li abundances accompanied by rather high rotational velocities or substantial nitrogen excess contradict theoretical predictions ; ( ii ) the relatively high-mass supergiants HR 461 and HR 8313 ( M > 6 M _ { \odot } ) with the detected abundances \log \epsilon = 1.3-1.5 . It is possible that the lithium in such stars was synthesized recently .