Autonomous shuttles have been used as end-mile solutions for smart mobility in smart cities. The urban driving conditions of smart cities with many other actors sharing the road and the presence of intersections have posed challenges to the use of autonomous shuttles. Round intersections are more challenging because it is more difficult to perceive the other vehicles in and near the intersection. Thus, this paper focuses on the decision-making of autonomous vehicles for handling round intersections. The round intersection is introduced first, followed by introductions of the Markov Decision Process (MDP), the Partially Observable Markov Decision Process (POMDP) and the Object-Oriented Partially Observable Markov Decision Process (OOPOMDP), which are used for decision-making with uncertain knowledge of the motion of the other vehicles. The Partially Observable Monte-Carlo Planning (POMCP) algorithm is used as the solution method and OOPOMDP is applied to the decision-making of autonomous vehicles in round intersections. Decision-making is formulated first as a POMDP problem, and the penalty function is formulated and set accordingly. This is followed by an improvement in decision-making with policy prediction. Augmented objective state and policy-based state transition are introduced, and simulations are used to demonstrate the effectiveness of the proposed method for collision-free handling of round intersections by the ego vehicle.