Density functional theory calculations have been performed to explore the mechanism of copper‐catalyzed hydroboration of 1,3‐diyne with HBpin. The catalytic cycles are composed of three elementary processes in succession, namely, the generation of copper hydride species, migratory insertion and σ‐bond metathesis, among which the σ‐bond metathesis step is rate‐determining with a free‐energy barrier of 19.7 kcal/mol. The syn‐addition selectivity originates from the high barrier for converting (Z)‐product to (E)‐product. Effects of diphosphine ligands and substituents on the reactivity were also addressed. Lastly, this copper‐catalyzed hydroboration was compared with a related ruthenium‐catalyzed one, and the obtained results indicated that copper‐catalyzed hydroboration has a more favorable σ‐bond metathesis step but more challenging migratory insertion step as compared to the ruthenium‐catalyzed counterpart. Wavefunction analyses were performed to understand the observed behaviors.