In this paper, we extend the framework of inverse optimal control to an inverse Stackelberg game (ISG) problem that involves a hierarchical two-player scenario. More specifically, the aim is to determine the unknown parameters in the leader’s and the follower’s objective functions based on their observed behavior in the final time window. Under a linear-quadratic setup, we first show that the parameter matrices in the objective functions for both the leader and the follower of the ISG are identifiable. Then, we propose a two-step approach to estimate the parameters in objective functions. In particular, the process first identifies the parameter matrix of the follower. Next, we identify the leader’s control gain within the final observation time window. Then we identify the leader’s matrix based on the identified leader’s control gain and the follower’s parameter matrix. Finally, we validate the effectiveness of our methodology through deterministic numerical experiments. (Figure presented.).