3D LiDAR based localization is a very common method for robot self-positioning on prior maps. Currently, few research works str focus on the failure detection of laser localization, which is a critical part in autonomous systems for mobile robots or intelligent vehicles. In this paper, we propose a statistical learning based method for localization failure detection, formulating the problem as a binary classification task. Specifically, we first extract features to measure the align quality of point clouds, which describe the geometric properties in local and global levels. Then a logistic regression model is trained and can detect the localization failures in new environments. We employ our self-collected dataset to demonstrate the effectiveness of the proposed method. The results show that the logistic regression model can achieve high accuracy on failure detection for 3D LiDAR based localization.