The target of this study is to describe the notion of 2-fuzzy metric spaces which is the extension of 2-metric space in the setting of that the area of triangle shaped by three distinct points is a convex, non-negative, normal and upper semi-continuous fuzzy number. For this aim, we first describe the notion of 2-fuzzy metric spaces, study some of their properties and give some examples. Then we investigate the relationship between 2-fuzzy metric spaces and 2-Menger spaces. Also, we discuss the triangle inequalities and its level forms in 2-fuzzy metric spaces. Finally, using the obtained properties and relationships we show that every 2-fuzzy metric induces a Hausdorff topology which is metrizable.