  In this paper, we study gradient Einstein-type structure immersed into a
Riemannian warped product manifold. We obtain some triviality results for the
potential function and smooth map $u$. We investigate conditions for a gradient
Einstein-type structure to be minimal, totally umbilical, or totally geodesic
immersed into a warped product $I\times_f M^n$. Furthermore, we characterize
rotational hypersurface into $\mathbb{R}\times_f\mathbb{R}^n$ has a gradient
Einstein-type structure.
