We present predictions at NLO accuracy in QCD for top-quark pair production induced by an anomalous chromomagnetic dipole moment of the top quark. Our results are obtained for total as well as fully differential cross sections, including matching to parton shower simulations. This process is expected to provide the most stringent direct limits on top-quark chromomagnetic dipole moment. We find that NLO corrections increase the contribution from the dipole moment by about 50\% at the LHC, and significantly reduce the renormalization and factorization scale dependence. Using the NLO prediction, we update the current limit from the Tevatron and the LHC measurements. Apart from total cross section, we also study other observables relevant for LHC phenomenology.