We study the dynamics of stellar-mass black holes (BHs) in star clusters, with particular attention to the formation of BH–BH binaries, which are interesting as sources of gravitational waves (GWs). We examine the properties of these BH–BH binaries through direct N-body simulations of Plummer clusters of N ≤ 105 low-mass stars with an initial population of stellar-mass BHs, using the nbody6 code. We find that the stellar-mass BHs segregate rapidly into the cluster core and form a dense subcluster of BHs in which BH–BH binaries form through three-body encounters. While most BH binaries are ejected from the cluster by recoils due to superelastic encounters with the single BHs, we find that for clusters with N ≳ 5 × 104, typically a few of them harden sufficiently so that they can merge via GW emission within the cluster. Also, for each of such clusters there are a few escaping BH binaries that merge within a Hubble time, with most merger times being within a few Gyr. These results imply that the intermediate-age massive clusters constitute the most important class of star cluster candidates that can produce dynamical BH–BH mergers at the present epoch. The BH–BH merger rates obtained from our computations imply a significant detection rate (~30 yr−1) for the proposed Advanced LIGO GW detector.