Catalysis of the reaction: S-adenosyl-L-methionine + histone H4 L-lysine (position 20) = S-adenosyl-L-homocysteine + histone H4 N6-methyl-L-lysine (position 20). This reaction is the addition of a methyl group to the lysine residue at position 20 of the histone H4 protein.
histone H4 lysine 20-specific methyltransferase activity