Deep learning techniques have been widely employed in semantic segmentation problems, especially in medical image analysis, for understanding image patterns. Skin cancer is a life-threatening problem, whereas timely detection can prevent and reduce the mortality rate. The aim is to segment the lesion area from the skin cancer image to help experts in the process of deeply understanding tissues and cancer cells' formation. Thus, we proposed an improved fully convolutional neural network (FCNN) architecture for lesion segmentation in dermoscopic skin cancer images. The FCNN network consists of multiple feature extraction layers forming a deep framework to obtain a larger vision for generating pixel labels. The novelty of the network lies in the way layers are stacked and the generation of customized weights in each convolutional layer to produce a full resolution feature map. The proposed model was compared with the top four winners of the International Skin Imaging Collaboration (ISIC) challenge using evaluation metrics such as accuracy, Jaccard index, and dice co-efficient. It outperformed the given state-of-the-art methods with higher values of the accuracy and Jaccard index.