In a stochastic Stackelberg asymmetric security game, the strong Stackelberg equilibrium (SSE) strategy is a popular option for the defender to get the highest utility against an attacker with the best response (BR) strategy. However, the attacker may be a boundedly rational player, who adopts a combination of the BR strategy and a fixed stubborn one. In such a condition, the SSE strategy may not maintain the defensive performance due to the stubbornness. In this paper, we focus on how the defender can adopt the unilateral-control zero-determinate (ZD) strategy to confront the boundedly rational attacker. At first, we verify the existence of ZD strategies for the defender. We then investigate the performance of the defender’s ZD strategy against a boundedly rational attacker, with a comparison of the SSE strategy. Specifically, when the attacker’s strategy is close to the BR strategy, the ZD strategy admits a bounded loss for the defender compared with the SSE strategy. Conversely, when the attacker’s strategy is close to the stubborn strategy, the ZD strategy can bring higher defensive performance for the defender than the SSE strategy does.