Cyclic-conjugated linkages between planar-macrocyclic molecules contribute to the robustness of the two-dimensional (2D)polymerization and extension of π-interactions.The fabrication of such linkages in 2D polymers remains challenging.Combining scanning tunneling microscope (STM) measurements and density functional theory (DFT) calculations,we demonstrate a linear polymerization of metal-free naphthalocyanine (NPc) molecules with[4]-radialene-like linkages on silver surfaces.Experimentally,by depositing NPc molecules on the Ag(110) surface and subsequent annealing up to 750 K,one-dimensional polymers are constructed along the[1(1)0]direction.High-resolution STM images show a stem-leaf-like feature.STM simulations based on a linear polymer of NPc molecules linked by four-membered carbon rings,[4]-radialene-like structure,agree well with the experimental observations.DFT calculations reveal that the polymerization process includes detaching two-terminal H atoms of NPc molecules along[1(1)0]direction,then bonding with a neighboring dehydrogenated NPc molecule by forming a four-membered ring.The dehydrogenation process can be promoted by on-surface impurities such as additional H atoms.Similar polymerizations have been achieved on Ag(111) surfaces in an amorphous way.Moreover,the energy gap of the NPc molecule decreases after linear polymerization,suggesting a red-shift for its optical absorption/scattering spectrum.Our study offers a new route to polymerize conjugated molecules with extended planar π-interactions.