An off-lattice dynamics Monte Carlo method is used to study the conformations of self-attractive semiflexible ring chains. The conformations depend mainly on the bending energy b and the self attractive interaction e of ring chains, and perfect helical structures are found in self-attractive semi flexible ring chains with the moderate attractive interaction E. Some monomers of the semiflexible ring chains wrap around the linearly aligned monomers and the size of helix is independent of chain length of ring chains. Coil-helix-globule transition occurs when the self-attractive interaction increases within semiflexibe ring chains, and the phase transition is attributed to the competition among the configurational entropy, the bending energy, and the self-attractive interaction. This study can help us understand the effects of topological constraints on the conformations and dynamical behaviors of polymer chains, and the importance of chain stiffness in biological systems and in the dynamics of DNA and protein folding. (C) 2017 Elsevier Ltd. All rights reserved.