Decline in strength is common in older persons but little data are available about its association with Alzheimer’s disease (AD). We studied the association of level of and rate of change in strength in 877 older persons without dementia at baseline and risk of AD. In a proportional hazards model adjusted for age, sex and education, each 1-lb decrease in grip strength at baseline was associated with about a 1.5% increase in the risk of AD (HR, 0.986; 95% CI, 0.973–0.998). These results persisted even after excluding persons who developed AD in the first 5 years of follow-up. In a subsequent model examining the association of the annual rate of change in grip strength with incident AD, each 1-lb annual decline in grip strength was associated with about a 9% increase in the risk of AD (HR, 0.915; 95% CI, 0.884–0.948). Results were similar after controlling for level and rate of change in body mass index, parkinsonian signs, physical and cognitive activity, depressive symptoms, vascular diseases and risk factors, social networks and early-life socioeconomic status. Declining strength in old age is associated with an increased risk of AD.