Specifically methylates the N1 position of guanosine-37 in various cytoplasmic and mitochondrial tRNAs. Methylation is not dependent on the nature of the nucleoside 5' of the target nucleoside. This is the first step in the biosynthesis of wybutosine (yW), a modified base adjacent to the anticodon of tRNAs and required for accurate decoding. guanosine(37) in tRNA + S-adenosyl-L-methionine = H(+) + N(1)-methylguanosine(37) in tRNA + S-adenosyl-L-homocysteine Monomer. Predominantly in the mitochondria and in the nucleus. Belongs to the class I-like SAM-binding methyltransferase superfamily. TRM5/TYW2 family.