Accurate cloud and shadow detection is a crucial prerequisite for optical remote sensing image analysis and application. Multi-temporal-based cloud and shadow detection methods are a preferable choice to detect clouds in complex scenes (e.g., thin clouds, broken clouds and clouds with interference from artificial surfaces with high reflectivity). However, such methods commonly require cloud-free reference images, and this may be difficult to achieve in time-series data since clouds are often prevalent and of varying spatial distribution in optical remote sensing images. Furthermore, current multi-temporal-based methods have limited feature extraction capability and rely heavily on prior assumptions. To address these issues, this paper proposes a Siamese network (Siamnet) for cloud and shadow detection based on Time-Series cloudy Images, namely TSI-Siamnet, which consists of two steps: 1) low-rank and sparse component decomposition of time-series cloudy images is conducted to construct a composite reference image to cope with dynamic changes in the cloud distribution in time-series images; 2) an extended Siamnet with optimal difference calculation module (DM) and multi-scale difference features fusion module (MDFM) is constructed to extract reliable disparity features and alleviate semantic information feature dilution during the decoder part. TSI-Siamnet was tested extensively on seven land cover types in the well-known Landsat 8 Biome dataset. Compared to six state-of-the-art methods (including four deep learning-based methods and two classical non-deep learning-based methods), TSI-Siamnet produced the best performance with an overall accuracy of 95.05% and MIoU of 84.37%. In three more challenging experiments, TSI-Siamnet showed enhanced detection of thin and broken clouds and greater anti-interference to highly reflective surfaces. TSI-Siamnet provides a novel strategy to explore comprehensively the valid information in time-series cloudy images and integrate the extracted spectral-spatial–temporal features for reliable cloud and shadow detection.