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In this paper, a packet scheduling scheme that supports real-time traffic with multi-level delay constraints in OFDMA systems is proposed. Under the delay constraint, a throughput enhancement is jointly studied. A mathematical model describes the differentiated behaviors of packet scheduling according to the delay constraint level, and a decision parameter is eventually derived and used in the determination of whether a given packet should be transmitted at current OFMDA transmit time interval (TTI) or would be tolerable for delay to the next TTI. Assuming that the packets violating the delay constraint are lost, the proposed scheme is evaluated in terms of the packet loss probability and throughput. It is then compared with existing schemes for real-time traffic support such as the exponential scheduling (EXP) scheme, the modified largest weighted delay first (M-LWDF) scheme, and the round robin scheme. The numerical results show that the proposed scheduling scheme performs much better than the aforementioned scheduling schemes in terms of the packet loss probability, with slightly larger throughput compared to the EXP and M-LWDF schemes.