A method of regulating blood glucose level and/or treating a diabetes is disclosed. The method includes administering a fusion peptide of a GLP-1 peptide and an Fc region. The Fc region is a hybrid Fc region containing a hinge region, a CH2 domain, and a CH3 domain from the N-terminal to the C-terminal direction, wherein the hinge region comprises a human IgD hinge region, the CH2 domain comprises a part of the amino acid residues of CH2 domain of human IgD and human IgG4, and the CH3 domain comprises a part of the amino acid residues of the human IgG4 CH3 domain, and has glycosylation at the IgD hinge region. The fusion peptide shows reduced side effects such as vomiting, nausea, and/or heart rate increase.
