Haploinsufficiency of the SCN1A gene encoding voltage-gated sodium channel NaV1.1 causes Dravet’s syndrome, a childhood neuropsychiatric disorder including recurrent intractable seizures, cognitive deficit and autism-spectrum behaviours. The neural mechanisms responsible for cognitive deficit and autism-spectrum behaviours in Dravet’s syndrome are poorly understood. Here we report that mice with Scn1a haploinsufficiency exhibit hyperactivity, stereotyped behaviours, social interaction deficits and impaired context-dependent spatial memory. Olfactory sensitivity is retained, but novel food odours and social odours are aversive to Scn1a+/− mice. GABAergic neurotransmission is specifically impaired by this mutation, and selective deletion of NaV1.1 channels in forebrain interneurons is sufficient to cause these behavioural and cognitive impairments. Remarkably, treatment with low-dose clonazepam, a positive allosteric modulator of GABAA receptors, completely rescued the abnormal social behaviours and deficits in fear memory in the mouse model of Dravet’s syndrome, demonstrating that they are caused by impaired GABAergic neurotransmission and not by neuronal damage from recurrent seizures. These results demonstrate a critical role for NaV1.1 channels in neuropsychiatric functions and provide a potential therapeutic strategy for cognitive deficit and autism-spectrum behaviours in Dravet’s syndrome.