Objective: To explore the relationship of family function with sleep and externalizing problem behaviors of preschool children, so as to provide a guidance for externalizing problem prevention and intervention among preschool children. Methods: From October 2023 to January 2024, a convenience sampling method was used to select 5 138 preschool children from kindergartens in 8 districts of Wuhan City, Hubei Province. Parents completed the survey for Family Adaptability and Cohesion Scale, children s sleep habits and Child Behavior Checklist (CBCL). Spearman correlation analysis was used to examine the correlation of family function with scores of sleep quality and externalizing problem behaviors among preschool children. A mediation model analysis and bootstrap test were conducted to further investigate the mediating role of sleep quality between family function and externalizing problem behaviors. Mplus 8.7 software was used for latent profile analysis of family function. Results: The reported rates of poor sleep quality and externalizing problem behaviors among preschool children were 11.8% ( n =607), 20.0% ( n =1 026). The relevant analysis results showed that family function was negatively correlated with sleep quality and externalizing problem behaviors ( r = -0.20, -0.23), and sleep quality was positively correlated with externalizing problem behaviors ( r =0.27) ( P <0.01). The mediation effect test showed that family function negatively predicted externalizing problem behaviors ( β =-0.079) and sleep quality ( β = -0.075), while sleep quality positively predicted externalizing problem behaviors ( β =0.215) ( P <0.01). The latent profile analysis results showed that family function could be classified into 4 categories: high family function group (23.01%), upper middle family function group (44.65%), moderate family function group (26.24%) and low family function group (6.11%). Compared to high family function, the other three categories significantly positively predicted externalizing problem behaviors, and the mediating effects of sleep quality on different categories of family function were statistically significant [upper middle family function: mediation effect value was 0.022 (95% CI =0.004-0.041) and direct effect value was 0.329 (95% CI =0.263-0.396); middle family function: mediation effect value was 0.087 (95% CI =0.063-0.115) and direct effect value was 0.491 (95% CI =0.416-0.565); low family function: mediation effect value was 0.144 (95% CI =0.107-0.185) and direct effect 0.621 (95% CI =0.503-0.740)] ( P < 0.05 ). Conclusion Family function negatively predicts the externalizing problem behaviors of preschool children, and sleep quality plays a partial mediating role.