Spontaneously hypertensive rats (SHR) show behavioural differences when compared to their strain-matched controls. These differences include decreased anxiety-like behaviour in SHR, while both improved performance and behavioural deficits have been reported in learning/memory studies. Considering that alterations in anxiety levels during the training session can modify retention performance in animal models of memory, the aim of the present study was to investigate the role of anxiety levels in the performance of SHR rats in the plus-maze discriminative avoidance task (PM-DAT), in which memory and anxiety are evaluated simultaneously. Adult (5-month-old) and young (45-day-old) SHR and normotensive Wistar rats (NWR) were treated with chlordiazepoxide (CDZ) or saline. Thirty minutes later, rats were submitted to the PM-DAT training session. After 24 h, the test session was performed. The results showed that: (1) adult SHR showed lower anxiety levels compared to adult NWR; (2) adult SHR and NWR, as well as young NWR, showed significant retention of the task, while young SHR showed impaired performance; (3) 5.0 mg/kg CDZ decreased anxiety levels in adult NWR and young and adult SHR; (4) 5.0 mg/kg CDZ impaired retention in adult SHR and NWR and increased retention in young SHR. Our data suggest an important role of anxiety levels in the performance of SHR in a plus-maze discriminative avoidance task.