In this paper, a novel vibration isolator based on a foldable cylinder with Kresling’s pattern is proposed, and the performance of the proposed isolator in terms of preventing structural vibration is numerically evaluated. It is known that foldable cylinders with Kresling’s pattern provide bi-stable folding motions under specific conditions. For simplification, a foldable cylinder with Kresling’s pattern is modeled using horizontal, longitudinal, and diagonal truss elements connected by rotational joints and enforced by Ramen frames, while maintaining the bi-stability of the structure. Additional linear springs are incorporated into the structure in order to obtain a nonlinear spring with quasi-zero-stiffness characteristics. It is numerically established that the combined structure (i) does not have resonant frequencies and (ii) decreases the vibration response even at high frequencies when it is used around the equilibrium position at which the spring stiffness is quasi-zero.