In normal rats, central administration of orexin or exposure to certain forms of stress can induce significant increases in blood pressure and sympathetic nerve activity, which can be blocked by orexin receptor antagonists. The resting blood pressure is, however, unaffected by such antagonists, but is significantly lower in rodents with total loss of orexin, such as prepro-orexin knockout mice and orexin neuron-ablated orexin/ataxin-3 transgenic rats. We hypothesize that orexin is involved in the pathophysiology and maintenance of high blood pressure in the spontaneously hypertensive rat (SHR), a model of primary hypertension. To test this hypothesis, we measured orexin-A mRNA expression in the rostral ventrolateral medulla and antagonized both orexin receptors using an orally administered potent dual orexin receptor antagonist, almorexant, in SHRs and normotensive Wistar–Kyoto rats. In SHRs, there was a strong trend towards an increased orexin-A mRNA expression in the rostral ventrolateral medulla, and blocking orexin receptors markedly lowered blood pressure (from 182/152 ± 5/6 to 149/119 ± 9/8 mmHg; P < 0.001), heart rate (P < 0.001), sympathetic vasomotor tone (P < 0.001) and the noradrenaline levels in cerebrospinal fluid and plasma (P < 0.002). The significant antihypertensive effects of almorexant were observed in wakefulness and non-rapid eye movement sleep during both dark and light phases of the diurnal cycle only in SHRs. Blocking orexin receptors had no effect on blood pressure and sympathetic tone in normotensive Wistar–Kyoto rats. Our study links the orexin system to the pathogenesis of high blood pressure in SHRs and suggests that modulation of the orexin system could be a potential target in treating some forms of hypertension.