In order to detect moving infrared dim and small target, a novel high-order cumulant projection algorithm was proposed. After background of infrared image sequence was suppressed, the normalized 3-order cumulant of temporal data was projected to 2-dimensions domain, and then target was detected by searching possible track in 2-dimensions domain. The statistic distribution expressions of target and noise in 2-dimensions domain were established. Compared with concerned algorithms, calculation load of the new algorithm is lower than that of other algorithms and detection rate of the new algorithm increases quickly with Signal-to-Noise Ratio (SNR) improvement. A simulation experiment with actual infrared image sequences was done to prove the validity of the new algorithm, and the targets with SNR no less than 2 and speed in image equal to 2 frames/pixel were successfully detected.