This paper deals with monocular SLAM of a mobile robot in an indoor environment where visually similar features (so-called indistinguishable features) exist on the ceiling. When these indistinguishable features exist near a feature, data association suffers from false matches which lead to localization failure. To reliably estimate the robot pose in various environments, the proposed scheme uses the additional information on whether the features are easily distinguishable (unique) or not. Then, a ceiling plane is estimated by the heights of the unique features to find the positions of the indistinguishable features approximately. Reliable data association is done by registering the indistinguishable features on the ceiling plane with small uncertainty regions which prevent the false matches. After this preprocess step, the data association results are used within the extended Kalman filter to estimate the robot pose. Corners and lamps are used as features in the experiments, and the results show that the proposed method successfully works in various indoor environments including indistinguishable features.