A variable-structure multiple-model (VSMM) approach, named equivalent-model augmentation (EqMA), is proposed. Here the model set is augmented by a variable model intended to best match the unknown true mode. To fully utilize the information provided by model sequences (model histories), this variable model depends on the true mode at the previous time. Thus different previous models correspond to different augmenting models. To make the estimation process computationally feasible, the unknown variable model at the previous time is approximated by an equivalent model (EqM) which provides the closest estimation results in the sense of minimum Kullback-Leibler (KL) divergence. EqM also contains the online information provided by the measurements. Performance of the proposed EqMA approach is evaluated via two scenarios of maneuvering target tracking. Simulation results demonstrate the effectiveness of EqMA compared with the interacting multiple-model (IMM) algorithm and the expected-mode augmentation (EMA) algorithm.