This disclosure provides a method of preventing, alleviating, or treating a condition (i.e., neutropenia) in a patient in need thereof, the condition characterized by compromised white blood cell production in the patient. The method includes administering to the patient a therapeutically effective amount of a protein complex comprising a modified human granulocyte-colony stimulating factor (hG-CSF) covalently linked to an immunoglobulin Fc region via a non-peptidyl polymer. The non-peptidyl polymer is site-specifically linked to an N-terminus of the immunoglobulin Fc region, and the modified hG-CSF comprises substitutions in at least one of Cys17 and Pro65.