The angle-sensitive photonic bandgap (PBG) is one of the typical features of one-dimensional photonic crystals. Based on the phase-variation compensation effect between the dielectric and hyperbolic metamaterials (HMMs), angle-insensitive PBGs can be realized in photonic hypercrystals. However, since hypercrystals are usually constructed using metal components, these angle-insensitive PBGs are mostly limited to narrow bandwidths in visible range. Here, we replace metal with indium tin oxide (ITO) to construct HMMs in the near-infrared range. In these ITO-based HMMs, we experimentally demonstrate the negative refraction of light in transverse magnetic polarization. With this HMM component, we realize a photonic hypercrystal with an angle-insensitive PBG in the wavelength range of 1.15-2.02 µm. These ITO-based hypercrystals with large angle-insensitive PBGs can find applications in near-infrared reflectors or filters.