This dissertation provides a theoretic study on the network security in general , the firewall in particular. In fact the firewall has been recognized as a very promising option to obtain the security inthe real work network environment . The dissertation provides a throuth theoretic investigation on the various problems raised in the computer network, and also explores a methodology of the security against IP spoofing. Moreover, it investigates a systematic procddure to make analysis and plans of the firewall configuration . Based on the above investigation and analysis, this dissertation provides two approaches to network security , which address anumber of issuesboth at the network and at applicatino level. At the network level, a new method is proposed which uses packet filtering based on the analysis of the counter plot about the screen router.On the other hand, at the application level, a novel method is explored which employs secureity software. Firewall-1 , on Bastion host. To demonstrate the feasibililty and the effectiveness of the proposed methodologties , a prototype implementation is made The experiment result shows that the screen router employing the proposed anti-IP spoofing method at the network level is effective enough for the system to remain secure without being invaded by any illegal packets entering form external hackers. Meanwhile , at the application level, the proposed software approach employing Firewall-1 is proved to be robust enugh to prevent hackings from the outer point the point protocal connnection . Theoretically, it is not possible to provide complete security to the network system, because the network security involve a number of issues raised form low level network equipments form high level network protocol. The result inthis dissertation provides a very promising solution to network security due to its high efficiency of the implementation and superb protectiveness from a variety of hacking.