University networks contain a variety of information that varies from highly lucrative patents to personal information. The purpose of this study was to develop a secure network model that will enhance network security for the institutions in the country. The study objectively seeks to determine the existing network models and network security model and assess their weaknesses, it also seeks to establish what hinders implementation of network security in these institutions. The content scope of the study includes 51 chartered universities in Kenya, ICT technical personnel responsible for managing network assets, resources and services were the respondents and the study was carried out over a period of one year. The study adopted a descriptive research design, the study utilized the five point Likert scale in designing questionnaires. Purposive sampling of the respondents in the study was carried out in the study due to the fact specific ICT personnel in the institutions could answer the questions. Out of the population of 51 institutions a sample size of 49 institutions was got from the use of normal approximation to the hyper geometric distribution. 255 questionnaires were sent out, with each institution having 5 questionnaires sent to it. Secondary data on SWOT analysis of network models and network security models were described, frequency and percentages of general characteristics of respondents were described then correlation analysis was carried out to determine the relationship of the variables used in the proposed model, then a regression analysis was performed. It was established network security models have flaws that needed addressing. The outcome of the research is a binary logistic regression equation model that was used to predict the network security status of university networks based on the implementation of the protection, detection, response and recovery mechanisms. The security model developed will assist universities to effectively implement security measures in their institutions so as to protect networks infrastructure. It is the researcher’s recommendation that training of staff on network security helps technical staff to have confidence in the network they are administering, so they are able to manage network-breaches in real time instead of reacting to attacks and also helps alleviate minor mistakes during normal work operations.