This invention relates to a process for polymerizing isobutene using a catalytic system comprising a transition metal compound, a benzene derivative compound, and methylaluminoxane, and the catalytic system applied to the polymerization of isobutene, (1) the added benzene derivative compound and methyl aluminoxane to the transition metal species provides higher stability of cation active site so that polyisobutene with a high molecular weight can be produced even at a higher reaction temperature than the conventional cationic polymerization temperature; (2) nonhalogen solvent such as toluene can be employed as a polymerization solvent instead of halogenated solvents such as methyl chloride; and (3) under the stable catalytic system, a final product with a high yield can be ensured for its long-term use.