We introduce graphene nanohelicoids, geometric analogues of graphene nanoribbons, in which the honeycomb lattice is embedded on a helicoidal surface. Starting from the three-dimensional helical structure, we construct effective one-dimensional lattice models with band structures characterized by a momentum-shifted particle–hole relation $E_v(k)=-E_c(k+\pi )$ that reflects an anti-chiral symmetry arising from the nonsymmorphic symmetry. A systematic investigation of graphene nanohelicoids using the tight-binding approximation reveals a number of trends upon varying width and edge orientation, for instance, alternating transitions between semiconducting and metallic regimes. As the structure width varies, the band gap periodically closes and reopens, accompanied by an alternating Zak phase that switches between trivial and nontrivial. Using an analytic tight-binding model with a continuous deformation of the graphene nanohelicoids, we explain the origin of width- and termination-dependent band inversion and alternating Zak phase, and derive the relationship between the termination-resolved index and the sublattice symmetry operator in one-dimensional nonsymmorphic systems.