Recent state-of-the-art methods for skin lesion segmentation are based on convolutional neural networks (CNNs). Even though these CNN-based segmentation approaches are accurate, they are computationally expensive. In this paper, we address this problem and propose an efficient fully convolutional neural network, named DermoNet. In DermoNet, due to our densely connected convolutional blocks and skip connections, network layers can reuse information from their preceding layers and ensure high accuracy in later network layers. By doing so, we take advantage of the capability of high-level feature representations learned at intermediate layers with varying scales and resolutions for lesion segmentation. Quantitative evaluation is conducted on three well-established public benchmark datasets: the ISBI 2016, ISBI 2017, and the PH2 datasets. The experimental results show that our proposed approach outperforms the state-of-the-art algorithms on these three datasets. We also compared the runtime performance of DermoNet with two other related architectures, which are fully convolutional networks and U-Net. The proposed approach is found to be faster and suitable for practical applications.