An electronic device with a rollable display may include the operations of: obtaining global burn-in information and local burn-in information according to a designated sampling period; on the basis of the result of analyzing the global burn-in information, predicting whether burn-in will at least partially occur in the entire area of a display area; when burn-in is predicted to at least partially occur in a boundary area, generating a first compensation map including pieces of local compensation data calculated to correspond to m block areas of the boundary area, respectively; when burn-in is predicted to at least partially occur in an area remaining after excluding the boundary area from the entire area, generating a second compensation map including pieces of global compensation data calculated to correspond to n block areas of the entire area, respectively; and controlling the rollable display to display image data compensated on the basis of the first compensation map or the second compensation map.