An authentication system having mobility in a public wireless LAN which processes authentication and charging through an authentication server of a wireless network operator, comprising: an access point (120; 140) wirelessly connected to a wireless terminal, for outputting an authentication request message or charging request message added with information of the wireless terminal and requesting authentication and charging of the wireless terminal, and receiving an authentication response message and controlling data transmission and reception of the authenticated wireless terminal; and an access point manager for receiving the authentication request message for the wireless terminal from the access point, confirming whether the wireless terminal has already been authenticated, transmitting the authentication request message to the authentication server of the wireless network operator and transmitting the received authentication response message to the access point (120; 140) when the wireless terminal has not been authenticated, and transmitting the authentication response message to the access point (120; 140) on the basis of the registered authentication information when the wireless terminal has been authenticated, wherein, when the access point manager confirms that the wireless terminal is newly authenticated, the access point manager adds new authentication information to the authentication response message, and transmits the resultant message to the access point (120; 140), wherein, when the wireless terminal has already been authenticated, the access point manager adds previous authentication information to the authentication response message, and transmits the resultant message to the access point (120; 140), wherein, when the wireless terminal is newly registered, the access point (120; 140) requests the access point manager to start charging, the access point (120; 140) transmits information through a charging start request, receives a start charging request response from the access point manager, and transmits wireless terminal status information to the access point manager; and wherein, when the access point (120; 140) confirms that the wireless terminal has already been registered, the access point (120; 140) does not request the access point manager to start charging but continuously enables data transmission and reception of the wireless terminal. an access point (120; 140) wirelessly connected to a wireless terminal, for outputting an authentication request message or charging request message added with information of the wireless terminal and requesting authentication and charging of the wireless terminal, and receiving an authentication response message and controlling data transmission and reception of the authenticated wireless terminal; and an access point manager for receiving the authentication request message for the wireless terminal from the access point, confirming whether the wireless terminal has already been authenticated, transmitting the authentication request message to the authentication server of the wireless network operator and transmitting the received authentication response message to the access point (120; 140) when the wireless terminal has not been authenticated, and transmitting the authentication response message to the access point (120; 140) on the basis of the registered authentication information when the wireless terminal has been authenticated, wherein, when the access point manager confirms that the wireless terminal is newly authenticated, the access point manager adds new authentication information to the authentication response message, and transmits the resultant message to the access point (120; 140), wherein, when the wireless terminal has already been authenticated, the access point manager adds previous authentication information to the authentication response message, and transmits the resultant message to the access point (120; 140), wherein, when the wireless terminal is newly registered, the access point (120; 140) requests the access point manager to start charging, the access point (120; 140) transmits information through a charging start request, receives a start charging request response from the access point manager, and transmits wireless terminal status information to the access point manager; and wherein, when the access point (120; 140) confirms that the wireless terminal has already been registered, the access point (120; 140) does not request the access point manager to start charging but continuously enables data transmission and reception of the wireless terminal.