We have synthesized novel chiral polymers containing a cinchona-based squaramide in the main chain. We designed a novel cinchona squaramide dimer that contains two cinchona squaramide units connected by diamines. The olefinic double bonds in the cinchona squaramide dimer were used for Mizoroki-Heck (MH) polymerization with aromatic diiodides. The MH polymerization of the cinchona squaramide dimer and aromatic diiodide proceeded well to give the corresponding chiral polymers in good yields. The catalytic activity of the chiral polymers was investigated for asymmetric Michael addition reactions. The effect of the squaramide structure of the polymeric catalyst on the catalytic performance is discussed in detail. We have surveyed the influence of the chiral polymer structure on the catalytic activity and enantioselectivity of the asymmetric reaction. The asymmetric Michael addition of β-ketoesters to nitroolefins was successfully catalyzed by polymeric cinchona squaramide organocatalysts to obtain the corresponding Michael adducts in good yields with excellent enantio- and diastereoselectivities. The polymeric catalysts were insoluble in commonly used organic solvents and easily recovered from the reaction mixture and reused several times without the loss of catalytic activity.