In this study, we propose a novel Light Detection and Ranging (LiDAR) sensor-based localization method for localization of a mobile robot. In localization using the LiDAR sensor, localization errors occur when real range measurements differ from reference distances computed from a map. This study focuses on three factors that cause differences between real range measurements and reference distances. The first factor corresponds to optical characteristics of the LiDAR sensor for objects such as glass walls and mirrors. The second factor corresponds to occlusions by dynamic obstacles. The third factor corresponds to static changes in the environment. In practical applications, three factors often simultaneously occur. Although there have been many previous works, robust localization to overcome these three difficulties is still a challenging problem. This study proposes a novel robust localization scheme that exploits only reliable range measurements. A LiDAR sensor-based localization scheme can be successfully executed by utilizing only a few reliable range measurements. Therefore, the computation of reliability plays a significant role. The computation of reliability is divided into two steps. The first step considers characteristics of optical sensors. The second step mainly deals with the effects of obstacles. The observation likelihood model exploits computed reliability for pose estimation. The proposed scheme was successfully verified through various experiments under challenging situations.