In recent years, the increasing incidence of morbidity of brain stroke has made fast and accurate segmentation of lesion areas from brain MRI images important. With the development of deep learning, segmentation methods based on the computer have become a solution to assist clinicians in early diagnosis and treatment planning. Nevertheless, the variety of lesion sizes in brain MRI images and the roughness of the boundary of the lesion pose challenges to the accuracy of the segmentation algorithm. Current mainstream medical segmentation models are not able to solve these challenges due to their insufficient use of image features and context information. This paper proposes a novel feature enhancement and context capture network (FECC-Net), which is mainly composed of an atrous spatial pyramid pooling (ASPP) module and an enhanced encoder. In particular, the ASPP model uses parallel convolution operations with different sampling rates to enrich multi-scale features and fully capture image context information in order to process lesions of different sizes. The enhanced encoder obtains deep semantic features and shallow boundary features in the feature extraction process to achieve image feature enhancement, which is helpful for restoration of the lesion boundaries. We divide the pathological image into three levels according to the number of pixels in the real mask area and evaluate FECC-Net on an open dataset called Anatomical Tracings of Lesions After Stroke (ATLAS). The experimental results show that our FECC-Net outperforms mainstream methods, such as DoubleU-Net and TransUNet. Especially in small target tasks, FECC-Net is 4.09% ahead of DoubleU-Net on the main indicator DSC. Therefore, FECC-Net is encouraging and can be relied upon for brain MRI image applications.