In this paper, the interrelations of some dynamical properties of a non-autonomous dynamical system (X, f1,∞) and its induced non-autonomous dynamical system (K (X), f1,∞) are studied, whereK (X) is the hyperspace of all non-empty compact subsets of X, endowed with Vietoris topology. Various stronger forms of sensitivity and transitivity are considered. Some examples of non-autonomous systems are provided to support the results. A relation between shadowing property of the non-autonomous system (X, f1,∞) and its induced system (K (X), f1,∞) is studied