The present invention relates to a novel glucagon derivative peptide, and a composition for preventing or treating hypoglycemia containing the novel glucagon derivative peptide as an active ingredient. The glucagon derivative according to the present invention has improved physical properties due to the change in isoelectric point (pI) while being capable of maintaining an activity on glucagon receptors, and thus can improve patient compliance when used as a hypoglycemic agent, and is also suitable for administration in combination with other anti-obesity agents. Accordingly, the glucagon derivative according to the present invention can be effectively used for the prevention and treatment of hypoglycemia and obesity.