New emerging applications for wireless sensor networks, such as mission-critical and multimedia applications, require sensing heterogeneous phenomena, and that the network supports different types of QoS-constrained traffic at variable rates. Designing an efficient medium access control protocol allowing these applications to work properly while coping with the limited resources of sensor networks is a challenging task. In this paper, we present a new adaptive MAC protocol with QoS support for heterogeneous wireless sensor networks which provides high channel utilization with a hybrid and adaptive behavior, and integrates a new efficient prioritization scheme to provide QoS support and fair data delivery of heterogeneous traffic. The protocol design is presented along with performance results obtained through extensive simulations. A mathematical model is provided and applied to perform an analytical evaluation of AMPH. Performance modeling, analysis, and simulation results show the effectiveness of our solution.