This paper investigates a box set-membership filter for nonlinear dynamic systems and on-line usage. To the best of our knowledge, although ellipsoid set-membership filter has more freedom degree to optimize a bounding estimation, it is computationally intractable to obtain an optimal prediction and update, and the approximation loss is uncertain in different scenarios. In this paper, we equivalently transform the prediction and update of the box set-membership filter to linear programing problems without loss of performance, respectively. Moreover, for a typical nonlinear dynamic system in target tracking, the remainder bound of the nonlinear function can be obtained analytically on-line. However, the ellipsoid bounding problem of the remainder usually needs to be relaxed to solve a semi-definite programming problem. Thus, the computational complexity of the optimal box set-membership filter is much less than that of the ellipsoid set-membership filter based on the semi-definite programming. Finally, a numerical example in target tracking demonstrates the effectiveness of the box set-membership filter. The proposed box set-membership filter can obtain a better trade-off between the filter accuracy and the computational complexity.