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In wireless mobile environments, large bandwidth and high quality of service (QoS) are recently required to support the increased demand for multimedia services. Long term evolution (LTE) is one of the promising solutions for the next generation broadband wireless access systems. In order to support high data rate with low latency, LTE simplifies network architecture and uses orthogonal frequency division multiple access (OFDMA) for downlink transmission technology. Packet scheduling algorithm is one of the important features to support QoS in LTE system. In this paper, we propose delay-aware packet scheduling (DAPS) algorithm considering QoS requirements of delays for various traffic classes, channel conditions, and fairness. To reflect delay experience at scheduling instance, DAPS algorithm observes how queue waiting time of head-of-line (HOL) packet is closed to allowed maximum packet delay. As a result, DAPS increases the number of transmitted packets with satisfying the required delay. Comprehensive simulation results show that DAPS algorithm yields better delay performance compared with two existing PF and M-LWDF algorithms.