Herein, we report a copper-catalysed site-selective thiolation of Csp³–H bonds of aliphatic amines. The method features a broad substrate scope and good functional group compatibility. Primary, secondary, and tertiary C–H bonds can be converted into C–S bonds with a high efficiency. The late-stage modification of biologically active compounds by this method was also demonstrated. Furthermore, the one-pot preparation of pyrrolidine or piperidine compounds via a domino process was achieved.