We present the results for the anomalous chromomagnetic moment of a quark at the one-loop and two-loop levels through model-independent parameterizations, considering the external gluon to be off-shell. Then, we consider different types of two-Higgs-doublet models with the momentum transfer of the external gluon, q2=±MZ2, and 0, for the numerical evaluations thereof for the top quark. We find that the contributions in the two-Higgs-doublet models are on the order of O(10−3) at the one-loop level and O(10−4) at the two-loop level, where the one-loop and two-loop contributions interfere destructively, resulting in the overall contributions being on the order of O(10−3) with a positive sign.