Site‐specific introduction of multiple components into peptides is greatly needed for the preparation of densely functionalized and structurally uniform peptides. In this regard, N‐terminal‐specific peptide modification is attractive, but it can be difficult due to the presence of highly nucleophilic lysine ε‐amine. In this work, we developed a method for the N‐terminal‐specific dual modification of peptides through a three‐component [3+2] cycloaddition with aldehydes and maleimides under mild copper catalysis. This approach enables exclusive functionalization at the glycine N‐terminus of iminopeptides, regardless of the presence of lysine ε‐amine, thus affording the cycloadducts in excellent yields. Tolerating a broad range of functional groups and molecules, the present method provides the opportunity to rapidly construct doubly functionalized peptides using readily accessible aldehyde and maleimide modules.