In this paper, a point-based Markov Decision Process (QMDP) algorithm is used for robust single-lane autonomous driving behavior control under uncertainties. Autonomous vehicle decision making is modeled as a Markov Decision Process (MDP), then extended to a QMDP framework. Based on MDP/QMDP, three kinds of uncertainties are taken into account: sensor noise, perception constraints and surrounding vehicles' behavior. In simulation, the QMDP-based reasoning framework makes the autonomous vehicle perform with differing levels of conservativeness corresponding to different perception confidence levels. Road tests also indicate that the proposed algorithm helps the vehicle in avoiding potentially unsafe situations under these uncertainties. In general, the results indicate that the proposed QMDP-based algorithm makes autonomous driving more robust to limited sensing ability and occasional sensor failures.