Background: Behavioural and psychological symptoms of dementia (BPSDs) are common. It is unclear whether associations are stronger with the absolute cognitive level or that relative to premorbid mental ability. Methods: The Neuropsychiatric Inventory (NPI) was administered to carers of patients with Alzheimer’s disease (AD). Patients underwent cognitive testing with the National Adult Reading Test (NART) to estimate premorbid IQ and 6 tests of current cognitive function. Results: 556 patients, mean age 77.3 years, had NPI scores. The total NPI score correlated significantly with most cognitive test scores, but multi-linear regression identified NART-IQ as the only significant cognitive predictor (β = –0.17, p = 0.008). Principal component analysis of the 10 NPI domains extracted 3 components corresponding to mood, frontal and psychotic factors. The NPI mood factor correlated significantly with NART-IQ (ρ = –0.14, p = 0.014) and lexical verbal fluency (ρ = –0.09, p = 0.034) only. The NPI frontal factor correlation with NART-IQ approached significance (ρ = –0.11, p = 0.053). The NPI psychotic factor correlated significantly with the Mini-Mental State Examination (ρ = –0.15, p < 0.001) and the Hopkins verbal learning test (ρ = –0.11, p = 0.013) scores. Conclusion: The relationship between BPSDs and cognition in AD is weak and largely explained by premorbid IQ. There is a stronger relationship between current cognition and psychotic symptoms.