The present invention provides a polypeptide which has: (i) an amino acid sequence wherein one or more amino acid residues are substituted in the region at positions 20 to 38 from the N terminus of the amino acid sequence shown in SEQ ID NO: 1; or (ii) an amino acid sequence wherein one or more amino acid residues are substituted in the region at positions 20 to 38 from the N terminus of the amino acid sequence shown in SEQ ID NO: 1 and one or more amino acid residues are deleted, substituted or added in the region at positions 1 to 19 or 39 to 294; and which has N-acetylglutamate kinase activity.