A media streaming home network system including at least one media client, which requests for a media streaming service through the Internet under a dynamic or static Internet Protocol (IP) environment, a media server, which detects network address information from the media client or a gateway connected to the media client, performs an access authentication process for the media client, and provides the media streaming service requested by the media client when the media client is authenticated, and a control server, which relays control messages transmitted between the media client and the media server, and provides the network address information of the media client to the media server. The media server can perform a process for authenticating the media client, using routing table information of the media client, without exchange of authentication information at an application level, even when both the media server and the media client use dynamic Internet Protocols (IPs), so that it is possible to rapidly and conveniently achieve the client authentication, while constructing a firm security system.