High harmonic generation (HHG) from solid-state crystals in strong laser fields has been understood by the band structure of the solids, which is based on the periodic boundary condition (PBC) due to translational invariance. For the systems with PBC due to rotational invariance, an analogous Bloch theorem can be applied. Considering a ring-type cluster of cyclo[18]carbon as an example, we develop a quasi-band model and predict the solid state-like HHG in this system. Under the irradiation of linearly polarized laser field, cyclo[18]carbon exhibits solid-state-like HHG originated from intra-band oscillations and inter-band transitions, which in turn is promising to optically detect the symmetry and geometry of controversial structures. Our results based on the Liouville-von-Neumann equations are well reproduced by the time-dependent density functional theory calculations and are foundational in providing a connection linking the HHG physics of gases and solids.