Catalysis of the transfer of a methyl group from S-adenosyl-L-methionine (AdoMet) to the alpha-amino group of the N-terminal amino or imino acid residue of a protein substrate. For example, yeast Tae1p and mammalian family member METTL11A preferentially modify the N-terminal residue of substrates with the N-terminal sequence X-Pro-Lys, where X can be Pro, Ala, or Ser.