Cloud detection is a prerequisite in many remote sensing applications, and it has been tackled through different approaches from simple thresholding to complicated deep network training. On the other hand, existing approaches are susceptible to failures while handling thin clouds, largely because of their small sizes, sparse distributions, as well as high transparency and similarity to the non-cloud background regions. This paper presents global context dense block U-Net (GCDB-UNet), a robust cloud detection network that embeds global context dense block (GCDB) into the U-Net framework and is capable of detecting thin clouds effectively. GCDB consists of two feature extraction units for addressing the challenges in thin cloud detection, namely, a non-local self-attention unit that extracts sample correlation features by aggregating the sparsely distributed thin clouds and a squeeze excitation unit that extracts channel correlated features by differentiating their importance. In addition, a dense connection scheme is designed to exploit the multi-level fine-grained representations from the two types of extracted features and a recurrent refinement module is introduced for gradual enhancement of the predicted classification map. We also created a fully annotated cloud detection MODIS dataset that consists of 1192 training images, 80 validation images and 150 test images. Extensive experiments on Landsat8, SPARCS and MODIS datasets show that the proposed GCDB-UNet achieves superior cloud detection performance as compared with state-of-the-art methods. Our created MODIS cloud detection dataset is available at https://github.com/xiachangxue/MODIS-Dataset-for-Cloud-Detection.