Complex evolutionary behavior of an age-structured predator-prey three-dimensional system has been investigated analytically as well as numerically. Natural populations, whose generations are non-overlapping, can be described by model of difference equations that explains how the populations evolve in discrete time steps. In this paper stability criteria of fixed points of 3-dimentional discrete model are discussed. Bifurcation diagrams of this map are drawn by varying one parameter while fixing value of other parameters. To examine complexity of the map during evolution, certain chaotic measures such as calculations of Lyapunov characteristic exponents (LCEs), topological entropies and correlation dimension have been done and represented graphically. © 2015 L. M. Saha and Neha Kumra.