A method of updating an IP address of an idle mode mobile subscriber station in an IP based broadband wireless access system and method of transmitting information for updating the IP address are disclosed. In updating an IP address of a mobile subscriber moving away into a second base station area from a first base station area in a broadband wireless access system, the present invention includes the steps of in the first base station area, entering an idle mode, in the second base station area, receiving information about an IP address update in the idle mode, and according to the received information, changing or retaining an IP address.