This paper presents fuzzy linguistic logic programming which is developed based on fuzzy logic programming introduced by P. Vojtas in order to facilitate the representation and reasoning on knowledge expressed in natural language. In fuzzy linguistic logic programming, truth values are linguistic terms such as true, very true, more or less true,and falsetaken from a hedge algebra of the truth variable, and linguistic hedges, e.g., very, more or less, quite,and rather, which are frequently used in natural language, can be used as unary connectives in formulae. In order to compute the truth value of a query, we provide a computational model which directly manipulates linguistic terms. The soundness of the computational model is proved. A fixpoint semantics of logic programs and the completeness of the computational model are discussed.