Unmanned aerial vehicles (UAVs) equipped with high definition (HD) cameras, intelligent sensors, computing, and communication modules can be deployed to execute crowdsensing tasks by leveraging federated learning (FL), e.g., air quality perception and ground target detection. FL can reduce transmission stress and protect data privacy when training models, which is suitable for resource constrained Internet of UAVs. Nevertheless, the incentive issues about information asymmetry and bounded rationality impede the applications of FL-enabled Internet of UAVs. The existing FL incentive approaches focus on the risk-free condition, where task publishers are capable of making decisions with complete rationality by utilizing expected utility theory. In fact, task publishers under risk conditions are often bounded rational, whose risk-awareness makes the utility models more sophisticated. To overcome the above problems, we present a prospect theory (PT)-based incentive mechanism for FL-enabled Internet of UAVs. We first leverage PT to model the task publisher’s risk-awareness behavior and construct the subjective utility model. Thereafter, we utilize the framing effect of PT to design the optimal contract to maximize the subjective utility. Simulation results demonstrate that, compared with the baseline method, the proposed incentive mechanism has better performance.