Passive acoustic monitoring is an increasingly important tool for whale research. Accurately detecting the end-point of whale whistle is an essential task in the study of marine mammal calls. However, the detection accuracy of the beluga whistle is reduced due to the non-stationary burst pulse interference in the marine environment. In this paper, an unsupervised two-stage beluga whistle end-point detection method is proposed to solve the above problem. Based on the high Q-factor wavelet decomposition, a rough whistle detection method is proposed to remove the silent time and the low intensity pulse. On this basis, local density adaptive spectral clustering is designed to further distinguish whistle and strong pulse interference based on the sparsity difference in time-frequency domain. The performance of the detector is tested with real signals of beluga whales, and its F 1-score is calculated. The result shows that the detector is obviously better than the traditional whistle detectors under the background of burst pulse interferences, and has higher robustness. In the future, the presented method is supposed to be applied for detecting whistles of some other whale species.