Immortal polymerization of epoxides with (5,10,15,20-tetraphenylporphinato)aluminum chloride ((TPP)AlCl, 1a) as the initiator coupled with alcohol or phenol as the protic chain-transfer agent (ROH) was dramatically accelerated by a sterically crowded organoaluminum compound such as methylaluminum bis-(2,6-di-tert-butyl-4-methylphenolate) (2a), affording polymers of controlled molecular weights with narrow distribution. The number of the polymer molecules (N(p)) is equal to the sum of the numbers of molecules of 1a (N(TPP)) and ROH (N(ROH)). By taking advantage of this acceleration method, the turnover number (N(p)/N(TPP)) of the immortal polymerization was increased up to 1000 under selected conditions.