Carboazidation of alkenes and alkynes holds the promise to construct valuable molecules directly from chemical feedstock therefore is significantly important. Although a few examples have been developed, there are still some unsolved problems and lack of universal methods for carboazidation of both alkenes and alkynes. Here we describe an iron-catalyzed rapid carboazidation of alkenes and alkynes, enabled by the oxidative radical relay precursor t-butyl perbenzoate. This strategy enjoys success with a broad scope of alkenes under mild conditions, and it can also work with aryl alkynes which are challenging substrates for carboazidation. A large number of diverse structures, including many kinds of amino acid precursors, fluoroalkylated vinyl azides, other specific organoazides, and 2H-azirines can be easily produced.