Autonomous driving technologies can provide better safety, comfort and efficiency for future transportation systems. Most research in this area has mainly been focused on developing sensing and control approaches to achieve various autonomous driving functions. Very little of this research, however, has studied how to efficiently handle sensing exceptions. A simple exception measured by any of the sensors may lead to failures in autonomous driving functions. The autonomous vehicles are then supposed to be sent back to manufacturers for repair, which takes both time and money. This paper introduces an efficient approach to make human drivers able to online teach autonomous vehicles to drive under sensing exceptions. A human-vehicle teaching-and-learning framework for autonomous driving is proposed and the human teaching and vehicle learning processes for handling sensing exceptions in autonomous vehicles are designed in detail. Experimental results acquired from a 1/10-scale autonomous driving vehicle illustrate the effectiveness and advantages of the proposed approach.