Poly[(tri-O-acetyl-D-glucal)-alt-(maleic anhydride)] was synthesized by free radical copolymerizations of the relevant comonomers. The alternating sequence of the copolymer was confirmed by $^1$H-NMR, elemental analysis, and titration of anhydride groups incorporated into the copolymer. Hydrolysis of the copolymer under different conditions resulted in poly[(2-acetoxymethyl-3,4-diacetoxytetrahydropyran-5,6-diyl) (1,2-dicarboxyethylene)] and poly[(2-hydroxymethyl-3,4-dihydroxytetrahydropyran-5,6-diyl) (1,2-dicarboxyethylene)]. The cytotoxicities of these polymers measured against normal and tumor cells (3LL, B16) in vitro were found to be higher than that of DIVEMA, a prototype polymer having a high antitumor activity.