Abstract Nuclear star clusters around a central massive black hole (MBH) are expected to be abundant in stellar black hole (BH) remnants and BH–BH binaries. These binaries form a hierarchical triple system with the central MBH, and gravitational perturbations from the MBH can cause high-eccentricity excitation in the BH–BH binary orbit. During this process, the eccentricity may approach unity, and the pericenter distance may become sufficiently small so that gravitational-wave emission drives the BH–BH binary to merge. In this work, we construct a simple proof-of-concept model for this process, and specifically, we study the eccentric Kozai–Lidov mechanism in unequal-mass, soft BH–BH binaries. Our model is based on a set of Monte Carlo simulations for BH–BH binaries in galactic nuclei, taking into account quadrupole- and octupole-level secular perturbations, general relativistic precession, and gravitational-wave emission. For a typical steady-state number of BH–BH binaries, our model predicts a total merger rate of ∼1–3 −3 −1, depending on the assumed density profile in the nucleus. Thus, our mechanism could potentially compete with other dynamical formation processes for merging BH–BH binaries, such as the interactions of stellar BHs in globular clusters or in nuclear star clusters without an MBH.