Sulfoxides are important functional molecules. We develop a short-route (one-pot) synthesis of this class of molecules by reacting thiols with alkenes or alkynes under mild and metal-free conditions. N-Fluorobenzenesulfonimide (NFSI) is used to play dual roles: as a radical initiator for a thiol-ene/-yne reaction to form sulfide adducts, and as efficient oxidant for conversion of the sulfides formed in situ to sulfoxides. Over-oxidation of the sulfoxides to sulfones is avoided in our approach.