Abstract In this paper we formulate multi-target tracking (MTT) as a rank-1 tensor approximation problem and propose an 1 norm tensor power iteration solution. In particular, a high order tensor is constructed based on trajectories in the time window, with each tensor element as the affifinity of the corresponding trajectory candidate. The local assignment variables are the 1 normalized vectors, which are used to approximate the rank-1 tensor. Our approach provides a flflexible and effective formulation where both pairwise and high-order association energies can be used expediently. We also show the close relation between our formulation and the multi-dimensional assignment (MDA) model. To solve the optimization in the rank-1 tensor approximation, we propose an algorithm that iteratively powers the intermediate solution followed by an 1 normalization. Aside from effectively capturing high-order motion information, the proposed solver runs effificiently with proved convergence. The experimental validations are conducted on two challenging datasets and our method demonstrates promising performances on both