In this article, we introduce the notion of cyclic generalized iterated function system (GIFS), which is a family of functions f(1), f(2), ..., f(M): X-k -> X, where each f(i) is a cyclic generalized phi-contraction (contractive) map on a collection of subsets {B-j}(j=1)(p) of a complete metric space (X, d) respectively, and k, M, p are natural numbers. When B-j, j = 1, 2, ..., p are closed subsets of X, we show the existence of attractor of this cyclic GIFS, and investigate its properties. Further, we extend our ideas to cyclic countable GIFS.