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 [11(_)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 [11(_)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.