Wireless capsule endoscopy (WCE) is a swallowable device used for screening different parts of the human digestive system. Automatic WCE image analysis methods reduce the duration of the screening procedure and alleviate the burden of manual screening by medical experts. Recent studies widely employ convolutional neural networks (CNNs) for automatic analysis of WCE images; however, these studies do not consider CNN's structural and computational complexities. In this paper, we address the problem of simplifying the CNN's structure. A low complexity CNN structure for bleeding zone detection is proposed which takes a single patch as input and then outputs a segmented patch of the same size. The proposed network is inspired by the FCN paradigm with a simplified structure. Since it is based on image patches, the resulting network benefits from moderate-sized intermediate feature maps. Moreover, the problem of redundant computations in patch-based methods is circumvented by non-overlapping patch processing. The proposed method is evaluated using the publicly available KID dataset for WCE image analysis. Experimental results show that the proposed network has better accuracy and AUC than previous structures while requiring less computational operations.