Electromagnetic wave propagations in a 3-dimensional (3D) left-handed (LH) metamaterial composed of periodic wired metallic spheres are studied numerically. It is shown that the metamaterial supports the dominant 3D LH wave with negative refractive indices. Parametric studies of dependencies of the dispersion characteristics on the unit cell structure are carried out and it is shown that the isotropy can be enhanced by tuning the diagonal wire diameter and the sphere diameters.