Zero-index metamaterials, distinguished by a near-zero effective refractive index, enable extraordinary wave-manipulation capabilities unattainable in conventional media. However, their practical implementation is fundamentally hindered by intrinsic radiative losses, as Dirac-cone modes residing within the light cone inevitably couple to free-space radiation, resulting in severe out-of-plane leakage and propagation attenuation. Here, we theoretically investigate and numerically demonstrate a terahertz metasurface that overcomes this bottleneck by embedding flat-band zero-index modes within topologically protected bound states in the continuum. Through meticulous engineering of the photonic band structure, we tailor an accidental triple degeneracy at the $\mathrm{\Gamma }$ point, forming a Dirac cone intersected by a flat band. The resulting modes simultaneously exhibit an effective zero refractive index, strongly suppressed out-of-plane radiation, divergent photonic density of states, and a polarization vortex singularity with topological charge dictated by the momentum-space topological invariant. We further verify that the topological polarization vortex and the near-zero-index response remain robust under continuous symmetry-preserving structural perturbations, and we assess practical integration feasibility through a substrate-supported configuration. Our findings establish a direct connection among zero-index photonics, topological optics, and flat-band physics, opening up perspectives for achieving low-loss extreme-parameter terahertz photonic platforms.

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• Bound states in the continuum
• Optical metamaterials
• Topological defects
• Topological effects in photonic systems
• Terahertz techniques