The inspection of gray matter (GM) tissue of the human spinal cord is a valuable tool for the diagnosis of a wide range of neurological disorders. Thus, the detection and segmentation of GM regions in magnetic resonance images (MRIs) is an important task when studying the spinal cord and its related medical conditions. This work proposes a new method for the segmentation of GM tissue in spinal cord MRIs based on deep convolutional neural network (CNN) techniques. Our proposed method, called MobileUNetV3, has a UNet-like architecture, with the MobileNetV3 model being used as a pre-trained encoder. MobileNetV3 is light-weight and yields high accuracy compared with many other CNN architectures of similar size. It is composed of a series of blocks, which produce feature maps optimized using residual connections and squeeze-and-excitation modules. We carefully added a set of upsampling layers and skip connections to MobileNetV3 in order to build an effective UNet-like model for image segmentation. To illustrate the capabilities of the proposed method, we tested it on the spinal cord gray matter segmentation challenge dataset and compared it to a number of recent state-of-the-art methods. We obtained results that outperformed seven methods with respect to five evaluation metrics comprising the dice similarity coefficient (0.87), Jaccard index (0.78), sensitivity (87.20%), specificity (99.90%), and precision (87.96%). Based on these highly competitive results, MobileUNetV3 is an effective deep-learning model for the segmentation of GM MRIs in the spinal cord.