In the last decade, numerous researches have been focused on Image Super-Resolution (SR); this recreation or improvement model is vital in different research areas. Recently, deep learning algorithm finds useful to advance in the resolution of the medical output. Here, we devise a novel Deep Convolutional Network model along with the optimal learning rate of the Rectified Linear Unit (ReLU) intended for Medical Image Super-Resolution (MISR). For getting the optimal values of Deep Learning AlexNet structure, Modified Crow Search (MCS) is utilized, which is mainly depends on the behavior of crow sets. The chosen Alexnet lacks in a sort of suitable supervision for upgrading execution of the proposed model that effectively aims to overfit. The proposed design, i.e., MISR, named Deep Optimal Convolutional AlexNet (DOCALN), derives the optimal values of learning rates of the ReLU activation function. Based on this optimal deep learning structure, the Low Resolution (LR) medical images can be applied. Experimentation results of our proposed model are compared with variants of Convolution Neural Networks (CNN) concerning different measures such as image quality assessment, SR efficiency analysis, and execution time. © 2020 - IOS Press and the authors. All rights reserved.