Spectral data, atmospheric parameters, and LTE metal abundances are presented for 22 massive(about 5 to 20 M.), Galactic, A-type supergiants. The atmospheric analysis of each star is performed using the most recent Kurucz LTE model atmospheres. Atmospheric parameters (T-eff, log g,xi) are determined from Mg I/II equilibrium and fitting theoretical H gamma line profiles; we chose the parameters where the loci of possible T-eff-gravity values from each indicator intersect. We show that non-LTE effects on the Mg I and Mg II abundances are small, but non-LTE can strongly affect Fe I abundances such that Fe I/II equilibrium is a poor atmospheric indicator. The metal abundances, calculated assuming LTE, are solar to within +/-0.2 dex. Overabundances of Na are found in the A-type supergiant atmospheres; we discuss this as a combination of possible non-LTE effects and/or pollution of newly synthesized Na from a NeNa proton capture reaction that could occur in the stellar core. Otherwise, we see no evidence of slight overall metal enrichments relative to solar in these young stars that might be expected owing to Galactic chemical evolution. These stars occupy an interesting position on the H-R diagram for the study of the evolution of massive stars. The data presented here shall be used to study the evolutionary status of these stars in an article in Part 1 of the Journal.