  In this paper we consider the Klebanov-Tseytlin background and its
non-Abelian T-dual geometry along a suitably chosen $SU(2)$ subgroup of
isometries. We analyse the Penrose limits along various null geodesics of both
the geometries. We observe that, the Klebanov-Tseytlin geometry does not admit
any pp-wave solutions. However, the T-dual background gives rise to pp-wave
solution upon taking the Penrose limit along some appropriate null geodesic. We
comment on the possible gauge theory dual for our pp-wave background.
