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This paper addresses the problem of robust speech endpoint detection in aircraft cockpit voice background. The proposed method described in this paper is based on a statistical model approach. Based on the voice background characteristics analysis, the complex Laplacian distribution model that directly aim at noisy speech is established; then the likelihood ratio test (LRT) based on binary hypothesis test is carried out; the decision rule of conventional maximum a posterior incorporating the inter-frame correlation lead to two separate thresholds, speech endpoint detection decision is finally made depend on the decision of previous frame and the observed spectrum. Experimental results show that the proposed method outperforms the typical method in robustness under the aircraft cockpit voice background.