Sleep problems, such as difficulty falling asleep, staying asleep, early awakening with failure to continue sleep, and altered sleep-wake cycle, are common in the general population. This cross-sectional study with 6,929 older adults (≥ 60 years) aimed to estimate the prevalence of different types of sleep problems, their associated factors, and the population-attributable fraction of associated factors among older adults. The outcome variables consisted of self-reported sleep problems: insomnia (initial, intermediate, late, and any type of insomnia), poor sleep quality, and daytime sleepiness. The independent variables were sociodemographic and behavioral characteristics and health conditions. The prevalence proportions were initial insomnia (49.1%), intermediate insomnia (49.2%), late insomnia (45.9%), any type of insomnia (58.6%), poor sleep quality (15.6%), and daytime sleepiness (38.4%). Female sex, presence of two or more chronic diseases, not eating the recommended amount of fruits and vegetables, and regular and bad/very bad self-rated health were positively associated with the sleep problems investigated. Consuming alcohol once a month or more was inversely associated with initial insomnia. Population attributable fraction estimates ranged from 3% to 19% considering two or more chronic diseases, not eating the recommended amount of fruits and vegetables, and regular and bad/very bad self-rated health. High prevalence of self-reported sleep problems was evinced in older adults. These results can be useful to guide public health services in the creation of informational, evaluative, and screening strategies for sleep problems in older Brazilian adults.