In this study, a new multi-band metamaterial structure is proposed based on a unit cell that has multiple U-shaped metal rings printed one inside the other. The number of distinct magnetic resonances is determined by the number of U-shaped rings placed in the unit cell. Using three rings in this paper, three distinct resonance frequencies can be shifted to desired values simply by changing the design parameters which are the metal width w, ring to ring separation s, arm length along y axis for each ring (h(in), h(mid), h(out)) as well as the material properties and dimension of the substrate. Transmission and reflection spectra of the proposed structure are obtained by using the CST Microwave Studio. Effects of the design parameters w, s, h(in) and h(mid) on the resonance behavior of the proposed structure are investigated in a comparative manner.