ABSTRACT There are challenges for cloud detection over bright surfaces, especially for Sentinel-2 image without thermal band. In this paper, we developed a new cloud detection algorithm for Sentinel-2 data designed to tackle the challenges of cloud detection on bright targets. Our algorithm (called RF-NDTeI-SNIC) was built through the integration of Random Forest (RF) model, Normalized Difference Temporal Index (NDTeI) cloud index and Simple Non-Iterative Clustering (SNIC) image segmentation algorithm. First, RF and NDTeI were used to derive the initial and second stage’s cloud detection results, respectively. Then, the RF- and NDTeI-based results were fused to remove the bright surfaces and land cover changes. Finally, the fusion results were further refined using SNIC for morphological processing. The proposed RF-NDTeI-SNIC algorithm was evaluated using nine challenging cloud-covered Sentinel-2 scenes with substantial bright surfaces. Results indicated that the average overall accuracy of our algorithm was 95.01%, with average commission rate of 10.19% for cloud. In addition, five commonly used Sentinel-2 cloud mask algorithms including s2cloudless, QA, Fmask, CDI and Tmask were selected for comparative analysis. Results suggested that our algorithm outperformed others with overall accuracies of 89.60–94.17% and cloud commission rate of 9.46–37.50%, and have significant advantages in terms of bright surfaces. In summary, the RF-NDTeI-SNIC algorithm we developed was capable of yielding accurate Sentinel-2 cloud masks, and the novel NDTeI cloud index we proposed gave a new and effective approach for improving the separability of clouds and bright surfaces.