In this paper, we study locally strongly convex centroaffine hypersurfaces with parallel cubic form with respect to the Levi–Civita connection of the centroaffine metric. As the main result, we obtain a complete classification of such centroaffine hypersurfaces. The result of this paper is a centroaffine version of the complete classification of locally strongly convex equiaffine hypersurfaces with parallel cubic form due to Hu et al. (J Differ Geom 87:239–307, 2011)