Polygenic scores can be used to distil the knowledge gained in genome-wide association studies for prediction of health, lifestyle, and psychological factors in independent samples. In this preregistered study, we used fourteen polygenic scores to predict variation in cognitive ability level at age 70, and cognitive change from age 70 to age 79, in the longitudinal Lothian Birth Cohort 1936 study. The polygenic scores were created for phenotypes that have been suggested as risk or protective factors for cognitive ageing. Cognitive abilities within older age were indexed using a latent general factor estimated from thirteen varied cognitive tests taken at four waves, each three years apart (initial n = 1091 age 70; final n = 550 age 79). The general factor indexed over two-thirds of the variance in longitudinal cognitive change. We ran additional analyses using an age-11 intelligence test to index cognitive change from age 11 to age 70. Several polygenic scores were associated with the level of cognitive ability at age-70 baseline (range of standardized β-values = -0.178 to 0.302), and the polygenic score for education was associated with cognitive change from childhood to age 70 (standardized β = 0.100). No polygenic scores were statistically significantly associated with variation in cognitive change between ages 70 and 79, and effect sizes were small. However, APOE e4 status made a significant prediction of the rate of cognitive decline from age 70 to 79 (standardized β = -0.319 for carriers vs. non-carriers). The results suggest that the predictive validity for cognitive ageing of polygenic scores derived from genome-wide association study summary statistics is not yet on a par with APOE e4, a better-established predictor.