Na metal is regarded as a potential anode material for next-generation Na metal batteries owing to its high theoretical capacity and low cost. However, the severe dendrite growth and infinitely volume changes of Na limit its practical applications as an anode material. In this study, a three-dimensional (3D) Cu foam skeleton with hierarchical ZnO nanorod arrays (CF@ZnO) was prepared as a stable host for dendrite-free Na metal anodes. Commercially available Cu foam was treated via a simple chemical precipitation method to grow hierarchical ZnO nanorod arrays, exhibiting a 3D porous structure with a cylindrical core-shell skeleton. The highly “sodiophilic” ZnO nanorod arrays provided abundant Na nucleation sites and exhibited low nucleation overpotential, which facilitated the homogeneous nucleation and uniform growth of Na on the electrode. Moreover, the 3D porous core-shell cylindrical structure of the nanorod arrays efficiently reduced the local effective current density, thus suppressing the growth of Na dendrites, as indicated by COMSOL Multiphysics simulations. As a result, the CF@ZnO electrode exhibited dendrite-free morphology during repeated Na plating/striping and excellent cycling stability with very small voltage hysteresis even at high current densities. When paired with a Na3V2(PO4)3 cathode, the CF@ZnO/Na electrode showed significant potential for application in full cells. This study provides a facile approach to design 3D sodiophilic hosts for high-energy-density Na metal batteries.