Dynamic resource allocation scheme is a key component of 3GPP long-term evolution (LTE) for satisfying quality-of-service (QoS) requirement as well as improving the system throughput. In this paper, a buffer-aware adaptive resource allocation scheme for LTE downlink transmission is proposed for improving the overall system throughput while guaranteeing the statistic QoS and keeping certain fairness among users. Specifically, the priorities of the users' data queues in the base station are ranked by their remaining life time or their queue overflow probability which is estimated by applying large deviation principle. An online measurement based algorithm which requires no statistical knowledge of the network conditions uses the queue priorities to dynamically allocate the resource blocks (RBs) for avoiding buffer overflow and providing statistic QoS guarantee. The simulation results show that the proposed algorithm improves the throughput and fairness while considerably reducing the average bit loss rate.