Specifically methylates the N1 position of guanosine-37 in various tRNAs. guanosine(37) in tRNA + S-adenosyl-L-methionine = H(+) + N(1)-methylguanosine(37) in tRNA + S-adenosyl-L-homocysteine Monomer. Belongs to the class I-like SAM-binding methyltransferase superfamily. TRM5/TYW2 family.