This paper proposes a novel approach to modeling linguistic fuzzy network flow using the hedge algebra framework. Traditional methods for network flow often struggle with handling vague or imprecise data, especially when linguistic terms are employed to describe capacity, cost, and flow. To address this, hedge algebra is applied to systematically represent and process the uncertainty inherent in linguistic variables. By leveraging the algebraic structure of linguistic terms, we construct a fuzzy network model that effectively captures the semantics of qualitative assessments and relationships. This method not only enhances the precision of fuzzy computations but also reduces computational complexity compared to traditional fuzzy set theory-based models. A maximum flow algorithm is developed to optimize flow within this linguistic fuzzy network, demonstrating the practicality and efficiency of the proposed model. Experimental results validate the model’s effectiveness in various network scenarios, highlighting its potential for applications in fields such as logistics, transportation, and supply chain management. Future work will focus on extending the approach to accommodate dynamic and multi-objective network problems, further enhancing its utility and scalability.