When a person makes a decision, it is automatically accompanied by a subjective probability judgment of the decision being correct, in other words, a confidence judgment. A better understanding of the mechanisms responsible for these confidence judgments could provide novel insights into human behavior. However, so far confidence judgments have been mostly studied in simplistic laboratory tasks while little is known about confidence in naturalistic dynamic tasks such as driving. In this study, we made a first attempt of connecting fundamental research on confidence with naturalistic driver behavior. We investigated the confidence of drivers in left-turn gap acceptance decisions in a driver simulator experiment (N = 17). We found that confidence in these decisions depends on the size of the gap to the oncoming vehicle. Specifically, confidence increased with the gap size for trials in which the gap was accepted, and decreased with the gap size for rejected gaps. Similarly to more basic tasks, confidence was negatively related to the response times and correlated with action dynamics during decision execution. Finally, we found that confidence judgments can be captured with an extended dynamic drift–diffusion model. In the model, the drift rate of the evidence accumulator as well as the decision boundaries are functions of the gap size. Furthermore, we demonstrated that allowing for post-decision evidence accumulation in the model increases its ability to describe confidence judgments in rejected gap decisions. Overall, our study confirmed that principles known from fundamental confidence research extend to confidence judgments in dynamic decisions during a naturalistic task.