We report a design and experimental realization of a three-dimensional (3D) acoustic double-zero-index medium (DZIM), whose effective mass density and compressibility are nearly zero simultaneously. The DZIM is constructed from a cubic lattice of three orthogonally-aligned metal rods in air. The combination of lattice symmetry and accidental degeneracy yields a four-fold degenerate point with conical dispersion at the Brillouin zone center, where the material becomes a 3D DZIM. Though occupying a finite volume, the 3D DZIM maintains the wave properties of a "void space" and enables rich applications. For demonstration, we fabricate an acoustic "periscope" by placing the designed 3D DZIM inside a 3D bending waveguide, and observe the unusual wave tunneling effect through this waveguide with undisturbed planar wavefront. Our findings establish a practical route to realize 3D DZIM as an effective acoustic "void space," which offers unprecedented opportunities for advanced sound manipulation.A wave propagating in a medium with one or more constitutive parameters vanishing does not accumulate any phase retardation. This characteristic can be leveraged for a number of unique wave functionalities such as wavefront engineering 1-10 , cloaking objects 8-14 , wave tunneling 15-23 , asymmetric transmission 24-26 and photonic/phononic doping [27][28][29][30][31][32] . A single-zero-index medium, with only one constitutive parameter near-zero, usually has a significant impedance mismatch with the background medium, which is undesirable for real applications. A double-zero-index medium (DZIM), with both constitutive parameters near-zero, can overcome this obstacle, owing to its finite-valued effective impedance 7-11 . In the past decade, various approaches have been proposed to