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A fast deterministic packet marking scheme (FDPM) for IP traceback against distributed denial of service attacks is presented, which applies a novel marking algorithm and significantly improves IP traceback in two aspects: (1) the victim doesn't need to accommodate fragments for recovery, so it needs several packets to identify an ingress router with lower false positives; (2) FDPM can scales to large distributed attacks with thousands of attackers. Theoretical analysis and the pseudo code are provided. Compared with previous DPM schemes, average convergence time of FDPM decreased by 86.3% packets or even more. Therefore FDPM is more efficient and represents a step forward in performance.