Although great success has been achieved in asymmetric fluoroalkylation reactions via nucleophilic or electrophilic processes, the development of asymmetric radical versions of this type of reactions remains a formidable challenge because of the involvement of highly reactive radical species. Here we report a catalytic asymmetric radical aminoperfluoroalkylation and aminodifluoromethylation of alkenes with commercially available fluoroalkylsulfonyl chlorides as the radical sources, providing a versatile platform to access four types of enantioenriched α-tertiary pyrrolidines bearing β-perfluorobutanyl, trifluoromethyl, difluoroacetyl and even difluoromethyl groups in excellent yields and with excellent enantioselectivity. The key to success is not only the introduction of the CuBr/chiral phosphoric acid dual-catalytic system but also the use of silver carbonate to suppress strong background and side hydroamination reactions caused by a stoichiometric amount of the in situ generated HCl. Broad substrate scope, excellent functional group tolerance and versatile functionalization of the products make this approach very practical and attractive.