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The IEEE 802.15.4 Medium Access Control (MAC) protocol is uniquely designed to meet the requirements of the low data-rate, low power-consumption applications in the Low Rate Wireless Personal Area Network (LR-WPAN). The analytical models of 802.15.4 MAC reported in the literature have been mainly developed under the assumptions of saturated traffic or non-bursty unsaturated traffic conditions. These assumptions are unable to capture the characteristics of bursty multimedia traffic. To fill this gap, this paper proposes a new analytical model for 802.15.4 MAC in LR-WPAN with bursty ON-OFF traffic. Quality-of-Service (QoS) performance metrics in terms of the throughput and total delay are derived. This analytical model is then adopted to investigate the QoS performance of 802.15.4 MAC under various traffic patterns, traffic loads, and number of stations. Numerical results show that the traffic patterns and traffic burstiness have a significant impact on the delay performance of 802.15.4 MAC.