The advanced computer network technology enables connectivity of computers through an open network environment. There has been growing numbers of security threat to the networks. Therefore, it requires intrusion detection and prevention technologies. In this paper, we propose a network based intrusion detection model using FCM(Fuzzy Cognitive Maps) that can detect intrusion by the DoS attack detection method adopting the packet analyses. A DoS attack appears in the form of the Probe and Syn Flooding attack which is a typical example. The SPuF(Syn flooding Preventer using Fussy cognitive maps) model captures and analyzes the packet informations to detect Syn flooding attack. Using the result of analysis of decision module, which utilized FCM, the decision module measures the degree of danger of the DoS and trains the response module to deal with attacks. For the performance comparison, the "KDD′99 Competition Data Set" made by MIT Lincoln Labs was used. The result of simulating the "KDD′99 Competition Data Set" in the SPuF model shows that the probe detection rates were over 97 percentages.