The mining parameters in most conventional data mining are numerical. Thus this paper attempts to propose a novel Web mining technique using linguistic minimum support and preference to discover interesting patterns from log data in Web servers. Linguistic minimum support and preference are characterized as fuzzy linguistic variables that are denoted by corresponding triangular fuzzy variables. The linguistic inputs and outputs are more natural and understandable for human beings. In addition, time duration on a Web page is considered and characterized as a fuzzy linguistic variable. The interesting traversal patterns with fuzzy linguistic variables make people easily understand the users' browsing paths and behaviors. The proposed algorithm thus discovers interesting traversal patterns with linguistic restriction. Experiments show accuracy and scalability of the algorithm.