Min-cost flow has been a widely used paradigm for solving data association problems in multi-object tracking (MOT). However, most existing methods of solving min-cost flow problems in MOT are either direct adoption or slight modifications of generic min-cost flow algorithms, yielding sub-optimal computation efficiency and holding the applications back from larger scale of problems. In this paper, by exploiting the special structures and properties of the graphs formulated in MOT problems, we develop an efficient min-cost flow algorithm, namely, minimum-update Successive Shortest Path (muSSP). muSSP is proved to provide exact optimal solution and we demonstrated its efficiency through 40 experiments on five MOT datasets with various object detection results and a number of graph designs. muSSP is always the most efficient in each experiment compared to the three peer solvers, improving the efficiency by 5 to 337 folds relative to the best competing algorithm and averagely 109 to 4089 folds to each of the three peer methods.