The underlying causes of late-Holocene climate variability in the tropics are incompletely understood. Here we report a 1,500-year reconstruction of climate history and glaciation in the Venezuelan Andes using lake sediments. Four glacial advances occurred between anno Domini (A.D.) 1250 and 1810, coincident with solar-activity minima. Temperature declines of −3.2 ± 1.4°C and precipitation increases of ≈20% are required to produce the observed glacial responses. These results highlight the sensitivity of high-altitude tropical regions to relatively small changes in radiative forcing, implying even greater probable responses to future anthropogenic forcing.