This paper proposes a deep learning image segmentation method for the purpose of segmenting wound-bed regions from the background. Our contributions include proposing a fast and efficient convolutional neural networks (CNN)-based segmentation network that has much smaller number of parameters than U-Net (only 18.1% that of U-Net, and hence the trained model has much smaller file size as well). In addition, the training time of our proposed segmentation network (for the base model) is only about 40.2% of that needed to train a U-Net. Furthermore, our proposed base model also achieved better performance compared to that of the U-Net in terms of both pixel accuracy and intersection-over-union segmentation evaluation metrics. We also showed that because of the small footprint of our efficient CNN-based segmentation model, it could be deployed to run in real-time on portable and mobile devices such as an iPad.