Multiple sclerosis (MS) lesion segmentation from MR imaging is a prerequisite step in clinical diagnosis and treatment of brain diseases. However, automated segmentation of MS lesions remains a challenging task, owing to the variant morphology and uncertain distribution of lesions across subjects. Despite the achieved success by existing methods, two problems still persist in automated segmentation of MS lesions, namely the lack of an effective feature enhancement approach for capturing locality context and the lack of global coherence in prediction for pixels. Hence, we propose a correlation learning network for both local and global context in this work. Specifically, we propose a sparse spatial correlation module to learn the spatial correlations within neighbours for local context. Besides, we propose a global coherence module to encode long-range dependencies for global context. The proposed method is evaluated on a public ISBI2015 datatset and a private in-house dataset collected from hospital. Experimental results show the competitive performance of our method against state-of-the-art methods.