Aging is accompanied by an increase in the probability of false memory. However, what role sleep plays in the age effect in false memory is less understood. Our study utilized a simplified conjoint recognition (SCR)-based Deese-Roediger-McDermott (DRM) paradigm to investigate the role of sleep on false memory in young and older adults. The results showed that sleep effect in false memory was modulated by age, manifested as sleep increased young adults' falsely recognized critical lures, while it reduced older adults'. In addition, in a more fine-grained analysis, the results of multinomial processing tree (MPT) modeling further revealed that young adults were more likely to retrieve memory based on gist traces than older adults, and young adults were more susceptible to guess a probe as "old" than older adults in the sleep condition. Combined findings from the number and ratio of falsely recognized critical lures and the MPT modeling, the current study suggested that sleep might increase young adults' false memory via gist extraction, while it decreased older adults' false memory via verbatim trace consolidation. The study contributes to a comprehensive view on the age-by-sleep effect on false recognition, with the segregation of cognitive components of verbatim memory, gist memory, and response bias.