In this paper, we design a three-dimensional isotropic left-handed metamaterial (LHM) composed of sphere-thorn shaped cells at visible frequencies. Adopting the metallic Drude's principle, we simulate and study its transmission properties for the incident plane electromagnetic wave. The dimension of unit cell here is far below the resonant wavelength, and thus the effective medium theory is well satisfied. With appropriate geometric parameters, this structure can realize negative refractive index with simultaneous negative permittivity and permeability at visible frequencies. The LHM proposed in this paper has advantages of simplicity and isotropy, moreover, our numerical model provides a new method for 'top-to-bottom’approach to preparing visible three-dimensional metamaterials.