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Under the context of quasi-metric, promoted the concept of interval-valued fuzzy metric space, the main results are as follows :(1) topology induced by quasi-metric is consistent with which induced via a standard interval-valued fuzzy quasi-metric; (2) proved that every quasi-metrizable topological space admits a compatible interval-valued fuzzy quasi-metric. On the contrary, topology generated by interval-valued fuzzy quasi-metric is quasi-metrizable; (3) discussed some properties of interval-valued fuzzy quasi-metric space which is bicompletion. proved that if an interval-valued fuzzy quasi-metric space has bicompletion, then it is unique up to isometry. In addition, we define a fuzzy contraction mapping of interval-valued fuzzy metric space, promote the Banach and Edelstein fixed point theorem to interval fuzzy metric space. [ABSTRACT FROM AUTHOR]