The present invention is directed to a method and an apparatus for use in a wireless communication system. Specifically, the present invention is directed to a method comprising: receiving essential System Information (SI) from a first cell, the essential SI including information for acquiring an on-demand SI; requesting the on-demand SI to the first cell; if the on-demand SI is not received from the first cell in a first specific period of time after the requesting the on-demand SI to the first cell is successful, re-requesting the on-demand SI to the first cell; and if the on-demand SI is not received from the first cell in a second specific period of time after a total number of requesting the on-demand SI to the first cell reaches a maximum value, re-selecting a second cell under assumption that the first cell is a barred cell, and an apparatus therefore.