A major reason leading to tracking failure is the spatial distractions that exhibit similar visual appearances as the target, because they also generate good matches to the target and thus distract the tracker. It is in general very difficult to handle this situation. In a selective attention tracking paradigm, this paper advocates a new approach of discriminative spatial attention that identifies some special regions on the target, called attentional regions (ARs). The ARs show strong discriminative power in their discriminative domains where they do not observe similar things. This paper presents an efficient two-stage method that divides the discriminative domain into a local and a semi-local one. In the local domain, the visual appearance of an attentional region is locally linearized and its discriminative power is closely related to the property of the associated linear manifold, so that a gradient-based search is designed to locate the set of local ARs. Based on that, the set of semi-local ARs are identified through an efficient branch-and-bound procedure that guarantees the optimality. Extensive experiments show that such discriminative spatial attention leads to superior performances in many challenging target tracking tasks.