Lung cancer is a dangerous non-communicable disease attacking both women and men and every year it causes thousands of deaths worldwide. Accurate lung nodule segmentation in computed tomography (CT) images can help detect lung cancer early. Since there are different locations and indistinguishable shapes of lung nodules in CT images, the accuracy of the existing automated lung nodule segmentation methods still needs further enhancements. In an attempt towards overcoming the above-mentioned challenges, this paper presents WEU-Net; an end-to-end encoder-decoder deep learning approach to accurately segment lung nodules in CT images. Specifically, we use a U-Net network as a baseline and propose a weight excitation (WE) mechanism to encourage the deep learning network to learn lung nodule-relevant contextual features during the training stage. WEU-Net was trained and validated on a publicly available CT images dataset called LIDC-IDRI. The experimental results demonstrated that WEU-Net achieved a Dice score of 82.83% and a Jaccard similarity coefficient of 70.55%.