The present invention relates to insulin and/or an insulin analogue conjugate, and a use thereof, wherein the insulin and/or insulin analogue have improved in vivo durability and stability by linking the same with an Fc region of immunoglobulin. The insulin and/or an insulin analogue conjugate of the present invention show an in vivo activity similar to that of insulin. In addition, the insulin and/or insulin analogue conjugate of the present invention are long-acting formulations of insulin and/or the analogue thereof, in which serum half-life is remarkably increased, and therefore, the present invention provides remarkable insulin and/or an insulin analogue conjugate, which do not induce hypoglycemia, a drawback of insulin treatment.