Recognizing human activities in a sequence is a challenging area of research in ubiquitous computing. Most approaches use a fixed size sliding window over consecutive samples to extract features---either handcrafted or learned features---and predict a single label for all samples in the window. Two key problems emanate from this approach: i) the samples in one window may not always share the same label. Consequently, using one label for all samples within a window inevitably lead to loss of information; ii) the testing phase is constrained by the window size selected during training while the best window size is difficult to tune in practice. We propose an efficient algorithm that can predict the label of each sample, which we call dense labeling, in a sequence of human activities of arbitrary length using a fully convolutional network. In particular, our approach overcomes the problems posed by the sliding window step. Additionally, our algorithm learns both the features and classifier automatically. We release a new daily activity dataset based on a wearable sensor with hospitalized patients. We conduct extensive experiments and demonstrate that our proposed approach is able to outperform the state-of-the-arts in terms of classification and label misalignment measures on three challenging datasets: Opportunity, Hand Gesture, and our new dataset.