  We present the Penrose limits of a complex marginal deformation of
$AdS_5\times S^5$, which incorporates the $SL(2,\mathbb{R})$ symmetry of type
IIB theory, along the $(J,0,0)$ geodesic and along the $(J,J,J)$ geodesic. We
discuss giant gravitons on the deformed $(J,0,0)$ pp-wave background.
