Compared with the traditional split-ring resonator reported by Pendry et al. (IEEE Trans. Microw. Theory Tech. 47:2075, 1999), the co-directional split-ring resonator, which has inherent low mutual coupling between its outer and inner rings, can provide distinct dual-band magnetic resonances. In this paper, we analyzed and compared different types of split-ring resonator, but selected the co-directional split-ring resonator for the tri-band magnetic resonator design because of its attractive dual-band magnetic resonance characteristics. We then accommodated the rings’ resonant strengths in the co-directional split-ring resonator to be nearly equal, and added an arm-loaded ring to design a new tri-band magnetic resonator. Finally, we designed and experimentally demonstrated a broadband μ-negative planar material with low frequency dispersion, which consisted of three pairs of tri-band magnetic resonators with slightly different dimensions.