To provide an easy-to-handle catalyst having high polymerization activity and hardly imparting an environmental load, and to provide a polymerization method using the catalyst, in cationic polymerization.

In this production method for a polymer, a boron trifluoride-tetrahydropyran complex is used as the cationic polymerization catalyst, and monomers (a vinyl ether compound, a styrene compound, an N-vinyl compound) each containing a double bond are polymerized. The cationic polymerization catalyst used for the method consists of the boron trifluoride-tetrahydropyran complex.