Video-based target tracking is a challenging task, because there always appears to be complex occlusion among the varying number of objects. Also, in practice, it is very common that the objects in a scene move irregularly with abrupt turns, which results in an interesting heavy-tailed phenomenon. As simulation has to run exceptionally long enough to capture the effect of the distribution tail, it is arduous to simulate heavytailed distribution. In this paper, we propose a new view to target tracking from a heavy-tailed perspective, establishing a simple but novel Multivariate Laplace Filter (MLF) tracking model, which efficiently and accurately describes the heavy-tailed issue and dramatically surmounts it. Some experimental results show the good performance of the proposed method.