In order to design optical metamaterials to surpass the limitation of unnaturally high refractive index in visible range, we propose the nanocylinders nanostructure with hexagonal close-packed arrangement to precisely control the electric and magnetic resonances, resulting in the manipulation of the effective index of metamaterials. By drastically increasing the strong capacitive coupling between nanocylinders and decreasing the diamagnetic effect with core-shell nanostructure, the unnaturally high refractive index of designed metamaterials can be achieved to be 10.5 in visible region. The diamagnetic effect of solid nanocylinders can be significantly suppressed by using the design strategy of hollow nanocylinders with higher order mode resonances, leading to great enhancement of the effective refractive index in broadband visible region. Expanding the refractive index into an unnaturally high positive region in visible range can complete the spectrum of attainable refractive index, and the high refractive index metamaterials can provide more design flexibility for nanophotonics.INDEX TERMS Metamaterial, high refractive index.