Abel-Grassmann’s groupoids, or shortly $AG$-groupoids, have been considered in quite a number of papers, although under the different names. In some papers they are named left-almost semigroups, $LA$-semigroups [3], in other left invertive groupoids [2]. In this paper we introduce the notions of a 3-potent element of an $AG$-groupoid and of $AG$-3-band. We describe $AG$-3-band as an $AG$-band of Abelian groups of a certain type. Furthermore we define mappings which take part in the construction that illuminates the structure of $AG$-3-bands. This construction defines the multiplication between the elements from different components, thus it gives the way how to make an $AG$-3-band.