Abstract: We generalize the notions of interval-valued fuzzy metric in the quasi-metric background,obtained that topology through the quasi-metric induced and through the standard interval-valued fuzzy quasi-metric induced is consistent.It is proved that every quasi-metrizable topological space admits a compatible interval-valued fuzzy quasi-metric.On the contrary,the topology generated by interval-valued fuzzy quasi-metric is quasi-metrizable.In addition,some properties of the bicomplete interval-valued fuzzy quasi-metric is discussed.It is proved that if there is an interval- valued fuzzy quasi-metric space which has bicompletion,then it is unique up to isometry.