Let G be a connected semisimple algebraic group of adjoint type over the field ℂ of complex numbers and B be a Borel subgroup of G. Let F be an irreducible projective B-variety. Then consider the variety E ∶= G ×B F, which has a natural action of G; we call it the G-induced variety or (G, B)-induced variety. In this article, we compute the connected component containing the identity automorphism of the group of all algebraic automor-phisms of some particular G-induced varieties E.