With the development of network computer system, the credibility of the network system becomes the key restrictive factor in its development. For this situation, a kind of interval intuitionistic fuzzy trust model of network computer system is proposed. Firstly, semantic tags of trust evaluation are mapped to the interval intuitionistic fuzzy numbers, which then are quantified so that the model can comprehensively describe ambiguity and completeness of semantic tags. Secondly, i interval intuitionistic fuzzy numbers and exact function are used to calculate trust value. Finally, the model algorithm is simulated experimently The results show that the model can evaluate the trust of network effevtively and rationally, which has certain theoretical significance.