We study chaotic motions of a classical string in a near Penrose limit of AdS₅×T^1,1. It is known that chaotic solutions appear on R×T^1,1, depending on initial conditions. It may be interesting to ask whether the chaos persists even in Penrose limits or not. In this talk, we would like to introduce basic tools for studying classical chaos first ,and then we would like to show our results. We revealed that sub-leading corrections in a Penrose limit provide an unstable separatrix, so that chaotic motions are generated as a consequence of collapsed Kolmogorov-Arnold-Moser (KAM) tori. Our analysis is based on deriving a reduced system composed of two degrees of freedom by supposing a winding string ansatz. Then, we provide support for the existence of chaos by computing Poincare sections.