Materials possessing an effective zero refractive index are often associated with Dirac-like cone dispersion at the center of the Brillouin zone (BZ). It has been reported the presence of hidden symmetry-enforced triply degenerate points [nexus points (NP)] away from the Brillouin zone center with the stacked dielectric photonic crystals. The spin-1 Dirac-like dispersion in the xy plane near the nexus point suggests a method for achieving zero refractive index materials. The stacked photonic crystals at the nexus points can be deemed as an effective moving double-zero-index medium (MDZIM) traveling with a speed relative to the laboratory reference. The ability of this moving double-zero-index medium to enable perfect wave tunneling across barriers without reflection has been demonstrated, dependent on the incident waves' specific angular orientations.