Methyl methacrylate was polymerized with Cp2YCl(THF) or IVB group metallocene compounds (i.e., Cp2ZrCl2 and Cp2HfCl2, etc.), in the presence of a Lewis acid like Zn(C2H5)(2). The Lewis acid was complexed with methyl methacrylate, which avoided the metallocene compounds being poisoned with a functional group. A living polymerization was promoted through the use of metallocene/MAO/Zn(C2H5)(2), which gave tactic poly(methyl methacrylate) with a high molecular weight. The polymer yield increases with polymerization time, which indicates that the propagation rate is zero in order in the concentration of the monomer. The polymer yield increases also with the concentration of Cp2YCl(THF), which indicates the yttrocene to be the real catalyst. When the polymerization temperature exceeds room temperature, the poly(methyl methacrylate) cannot be synthesized by the Cp2YCl(THF) catalyst. When the reaction temperature reachs -60 degrees C, the poly(methyl methacrylate) is high syndiotatic and molecular weight by the Cp2YCl(THF)/MAO catalyst system.