Aims.To investigate any correlation between Li abundances and rotational velocities among F-G evolved stars, we study a large sample of early F stars from the Bright Star Catalogue (BSC), most of them classified in the literature as giant stars.Methods.Physical parameters and Li abundances are estimated for each star, often for the first time, by comparing observed and synthetic spectra. We analyse the position of the stars in the H-R Diagram based on Hipparcos data using stellar evolutionary tracks and we discuss their Li abundances and projected rotational velocities.Results.Observed stars are mostly on the turnoff, with masses between 1.5 and 2.0 M?. The stars with measured A(Li) abundance show high Li content, most of them with abundance near the cosmic value. The A(Li) versus V sin i diagram shows the same trend as reported in previous studies: fast rotators (V sin igse 30 km s-1) are also stars with high Li content, whereas slow rotators present a wide range of values of A(Li), ranging from no detected Li to the cosmic value.