Catalysis of the reaction: S-adenosyl-L-methionine + histone H3 L-lysine (position 37) = S-adenosyl-L-homocysteine + histone H3 N6-methyl-L-lysine (position 37). This reaction is the addition of a methyl group to the lysine residue at position 37 of the histone H3 protein.
histone-H3K37 methyltransferase activity