Psychological well-being is a crucial aspect of the psychological functioning of parents with young children, as it relates to an individual's ability to accept themselves, build positive relationships, manage their environment, maintain life goals, and develop their potential. In fulfilling their parenting roles, parents face various demands that can increase parenting stress, whereas self-efficacy can serve as a psychological resource helping individuals cope with these demands. This study aimed to analyze the influence of parenting stress and self-efficacy on psychological well-being and to examine the mediating role of self-efficacy in the relationship between parenting stress and psychological well-being among parents of young children. A quantitative approach was employed using Structural Equation Modeling–Partial Least Squares (SEM-PLS) analysis. The results indicate that parenting stress has a significant negative effect on both psychological well-being (β = −0.273; p < 0.001) and self-efficacy (β = −0.363; p = 0.001). Conversely, self-efficacy has a significant positive effect on psychological well-being (β = 0.384; p = 0.001). Analysis of the indirect effect reveals that self-efficacy significantly mediates the relationship between parenting stress and psychological well-being (β = −0.139; p = 0.001). The research model explains 29.8% of the variance in psychological well-being. These findings demonstrate that the psychological well-being of parents with young children is linked not only to the level of parenting stress but also to their belief in their own ability to handle parenting demands. Therefore, strengthening self-efficacy and managing parenting stress should be addressed concurrently to support the psychological well-being of parents with young children.