Catalyzes the transfer of the gamma-phosphate of ATP to D-galactose to form alpha-D-galactose-1-phosphate (Gal-1-P). alpha-D-galactose + ATP = ADP + alpha-D-galactose 1-phosphate + H(+) Carbohydrate metabolism; galactose metabolism. Was identified as a high-confidence drug target. Belongs to the GHMP kinase family. GalK subfamily.