Efficient intersection planning is one of the most challenging tasks for an autonomous vehicle at present. Politeness to other traffic participants and reaction to surrounding information are the key aspects that determine the performance of planning algorithm for an autonomous vehicle. In order to capture these aspects, we propose a planning framework, based on the partially observable Markov decision process (POMDP), to ensure social compliance and optimize the motion response of autonomous vehicles. The framework designs a novel POMDP model to ensure effective prediction of behavioral intentions and decision-making at intersections with no traffic signs and low traffic volume. Then, a deterministic planner is employed as the baseline to realize planning. Specifically, we consider both the driving position and the facing angle of the vehicle in real-world situations. At the same time, we utilize scattering methods for probability updating and intent determination to improve the algorithm’s adaptability to real-world scenarios. The proposed framework is evaluated in different scenarios to demonstrate its capabilities in terms of the interactive planning for an autonomous vehicle.