A non-olefinic monomer, methyl 1-bicyclobutanecarboxylate (MBC), was successfully polymerized by the controlled/"living" atom transfer radical polymerization (ATRP) technique, resulting in a well-defined homopolymer, PMBC, with only cyclobutane ring units in the polymer chain. An AB block copolymer poly(methyl 1-bicyclobutanecarboxylate)-b-polystyrene (PMBC-b-PS), having an all-ling unit segment, was also synthesized with narrow polydispersity and designed number-average molecular weight in addition to precise end groups. The H-1 NMR spectra, glass-transition temperature, and thermal stability of PMBC, PMBC-b-PS, and PS-b-PMBC were investigated. The experimental results showed that the cyclobutane rings in the two block polymers improved their thermal stability.