As autonomous vehicles begin venturing on the urban road, rational decision making is essential for driving safety and efficiency. This paper presents a situation-aware decision making algorithm for autonomous driving on urban road. Specifically, an urban road situation model is proposed first for proper environment representation, thereafter the situation-aware decision making problem is modeled as a Partially Observable Markov Decision Process (POMDP) and solved in an online manner. The proposed algorithm has been extensively evaluated, which is general enough for autonomous driving in various urban road scenarios, including leader following, collision avoidance and traffic negotiation at both T-junction and roundabout.