Landslides may obstruct river flow and result in landslide dams; they occur in many regions of the world. The formation and disappearance of natural lakes involve a complex earth-surface process. According to the lessons learned from many historical cases, landslide dams usually break down rapidly soon after the formation of the lake. Regarding hazard mitigation, prompt evaluation of the stability of the landslide dam is crucial. Based on a Japanese dataset, this study utilized the logistic regression method and the jack-knife technique to identify the important geomorphic variables, including peak flow (or catchment area), dam height, width and length in sequence, affecting the stability of landslide dams. The resulting high overall prediction power demonstrates the robustness of the proposed logistic regression models. Accordingly, the failure probability of a landslide dam can also be evaluated based on this approach. Ten landslide dams (formed after the 1999 Chi-Chi Earthquake, the 2008 Wenchuan Earthquake and 2009 Typhoon Morakot) with complete dam geometry records were adopted as examples of evaluating the failure probability. The stable Tsao-Ling landslide dam, which was induced by the Chi-Chi earthquake, has a failure probability of 27.68% using a model incorporating the catchment area and dam geometry. On the contrary, the Tangjiashan landslide dam, which was artificially breached soon after its formation during the Wenchuan earthquake, has a failure probability as high as 99.54%. Typhoon Morakot induced the Siaolin landslide dam, which was breached within one hour after its formation and has a failure probability of 71.09%. Notably, the failure probability of the earthquake induced cases is reduced if the catchment area in the prediction model is replaced by the peak flow of the dammed stream for these cases. In contrast, the predicted failure probability of the heavy rainfall-induced case increases if the high flow rate of the dammed stream is incorporated into the prediction model. Consequently, it is suggested that the prediction model using the peak flow as causative factor should be used to evaluate the stability of a landslide dam if the peak flow is available. Together with an estimation of the impact of an outburst flood from a landslide-dammed lake, the failure probability of the landslide dam predicted by the proposed logistic regression model could be useful for evaluating the related risk.