Using a thalamocortical computational model of absence epilepsy, we consider the linear delayed feedback control (LDFC) as a brain stimulation strategy for seizure suppression. The model consists of a pyramidal cell population (PY) and an interneuron population (IN) in the cortex and thalamocortical relay cells (TC) and reticular nucleus (RE) in the thalamus. Without control, the system behaves spike-and-wave discharges (SWDs). The typical LDFC with a constant feedback gain and a constant time delay, can effectively suppressed seizures only in a certain range of the parameter space. We propose to use a periodic time delay instead. The seizure can be effectively suppressed in almost the full parameter space. The underlying control mechanisms are also demonstrated. We recommend the LDFC with periodic time delays as a potential deep brain stimulation (DBS) therapy for absence epilepsy.