  Considering the holographic dark energy (HDE) with two different Infrared
(IR) cutoffs, we study the evolution of a cyclic universe which avoids the
Big-Rip singularity. Our results show that, even in the absence of a mutual
interaction between the cosmos sectors, the HDE model with the Hubble radius as
IR cutoff can mimics a cosmological constant in the framework of a cyclic
cosmology. In addition, we find that both the interacting and non-interacting
universes may enter into a cycle of sequential contraction and expansion, if
the Granda-Oliveros (GO) cutoff is chosen as the IR cutoff in the energy
density of the HDE.
