Network intrusion anomaly detection technique has been widely employed in computer network environments as a highly effective security prevention method. As network technology and network applications have advanced at a rapid pace, so too has network data traffic, resulting in an increase in virus and attack kinds. In the face of large-scale traffic and characteristic information, traditional intrusion detection will have problems such as low detection accuracy, high false negatives, and reliance on dimensionality reduction algorithms. Therefore, it is particularly important to establish a fast and efficient network intrusion anomaly detection method to deal with the current complex network environment. This work designs a computer network intrusion detection model with a recurrent neural network in order to explore a new intrusion detection method. The main purpose of this article include the following: (1) design a network security emergency response system architecture with the recurrent neural network model. This system consists of a management center module, a knowledge database module, a data acquisition module, a risk detection tool module, a risk analysis and processing module, a data protection module, and a remote connection auxiliary module. The modules cooperate with each other to complete system functions. (2) Aiming at the risk analysis and processing module, a network intrusion detection model combining bidirectional long short-term memory (BiLSTM) and deep neural network (DNN) is designed. In view of the lack of consideration of the before-and-after relevance of intrusion data features and the multifeature problem in existing models, the use of BiLSTM to extract the relevance between features and the use of DNN to extract deeper features are proposed. Aiming at the problem that the model lacks consideration of the importance of features, it is proposed to embed an attention mechanism into the network to increase consideration for the importance of features. (3) Massive experiments have verified the reliability and effectiveness of the method proposed in this work.