Human decision-making is underpinned by distinct systems that differ in flexibility and associated cognitive cost. A widely accepted dichotomy distinguishes between a cheap but rigid model-free system and a flexible but costly model-based system. Typically, humans use a hybrid of both types of decision-making depending on environmental demands. However, children's use of a model-based system during decision-making has not yet been shown. While prior developmental work has identified simple building blocks of model-based reasoning in young children (1-4 years old), there has been little evidence of this complex cognitive system influencing behavior before adolescence. Here, by using a modified task to make engagement in cognitively costly strategies more rewarding, we show that children aged 5-11-years (N = 85), including the youngest children, displayed multiple indicators of model-based decision making, and that the degree of its use increased throughout childhood. Unlike adults (N = 24), however, children did not display adaptive arbitration between model-free and model-based decision-making. Our results demonstrate that throughout childhood, children can engage in highly sophisticated and costly decision-making strategies. However, the flexible arbitration between decision-making strategies might be a critically late-developing component in human development.