High-order motion information is important in multi-target tracking (MTT) especially when dealing with large inter-target ambiguities. Such high-order information can be naturally modeled as a multi-dimensional assignment (MDA) problem, whose global solution is however intractable in general. In this paper, we propose a novel framework to the problem by reshaping MTT as a rank-1 tensor approximation problem (R1TA). We first show that MDA and R1TA share the same objective function and similar constraints. This discovery opens a door to use high-order tensor analysis for MTT and suggests the exploration of R1TA. In particular, we develop a tensor power iteration algorithm to effectively capture high-order motion information as well as appearance variation. The proposed algorithm is evaluated on a diverse set of datasets including aerial video sequences containing ariel borne dense highway scenes, top-view pedestrian trajectories, multiple similar objects, normal view pedestrians and vehicles. The effectiveness of the proposed algorithm is clearly demonstrated in these experiments.