Organic polymers may present magnetic ordering, which attracts more attention of both theoretical and experimental researchers. From the structural analysis experiment, the magnetic organic polymers may show the diamond-like chain. Usually they are abstracted as the mixed spin-1/2 and 1(or 2) Ising model, which is given in Fig.1. Ji(Jb>0, Jab<0) is the nearest-neighbor exchange couplings. For example, Rajca et al have designed a magnetic organic polymer with a large density of cross-links S=1/2 and alternating connectivity of radical S = 2 modules[1]. The magnetic properties of the organic polymers have been studied by various methods. By the Monte Carlo simulation spin frustration-related behavior of mixed spin-1/2 and 1 Ising diamond chain has been investigated. Magnetization with different antiferromagnetic exchange coupling is simulated under magnetic field. They found the dimmer and trimmer states [2]. Using the many-body Green's function method magnetic properties of organic polymers with diamond-like chain are discussed. The results reveal the sublattice magnetizations of the two polymers are both smaller than their classical spin values. The ground state magneizations of them are also smaller than their predicted values in the antiferromagnettic exchange coupling case. Among these techniques, there is an efficient method called the effective field theory (EFT) without introducing mathematical complexities. We have successfully applied this method to the magnetic properties of the nanoparticle, the nanowire, the nanotube etc[3]. Here, we shall intend to continue to apply this theory (EFT) to study the magnetic properties of the organic polymer. Particular interest has been devoted to study low-temperature magnetization showing step-like plateau and the effects of anisotropy on the organic polymer diamond chain.