Refractive index is the most important property of material in optics and most naturally existing transparent materials possess small positive indices of refraction. With the progress of metamaterials, we can manipulate the electromagnetic properties of materials. Meta- materials promise unexpected physical phenomena through creating artificial “atoms” with an array of period metallic structure. However most researches are focusing on the negative re- fractive index materials at present, on the contrary the opposite side of high refractive index materials attracts far less attention. Previous approaches using metamaterials were not success- ful in realizing broadband isotropy high refractive indices. Here we design a broadband, isotropy three-dimensional metamaterial with extremely high index of refraction in terahertz region which composed of strongly coupled unit cells. We increase the effective permittivity through strong capacitive coupling and decrease the diamagnetic response with a thin metallic structure in the unit cell. A peak refractive index of 67.9 at 2.14 THz is observed under TE mode and a peak refractive index of 66.9 at 2.16 THz under TM mode. Both of polarizations maintain low loss with figure of merit go to as high as 2.12 and 2.48 separately. Moreover, the refractive index does not fall sharply at higher frequencies, and shows an extremely broadband behavior with a full-width at half-maximum (FWHM) of more than 2 THz.