Each stage of sleep can affect human health, and not getting enough sleep at any stage may lead to sleep disorder like parasomnia, apnea, insomnia, etc. Sleep-related diseases could be diagnosed using Convolutional Neural Network Classifier. However, this classifier has not been successfully implemented into sleep stage classification systems due to high complexity and low accuracy of classification. The aim of this research is to increase the accuracy and reduce the learning time of Convolutional Neural Network Classifier. The proposed system used a modified Orthogonal Convolutional Neural Network and a modified Adam optimisation technique to improve the sleep stage classification accuracy and reduce the gradient saturation problem that occurs due to sigmoid activation function. The proposed system uses Leaky Rectified Linear Unit (ReLU) instead of sigmoid activation function as an activation function. The proposed system called Enhanced Sleep Stage Classification system (ESSC) used six different databases for training and testing the proposed model on the different sleep stages. These databases are University College Dublin database (UCD), Beth Israel Deaconess Medical Center MIT database (MIT-BIH), Sleep European Data Format (EDF), Sleep EDF Extended, Montreal Archive of Sleep Studies (MASS), and Sleep Heart Health Study (SHHS). Our results show that the gradient saturation problem does not exist anymore. The modified Adam optimiser helps to reduce the noise which in turn result in faster convergence time. The convergence speed of ESSC is increased along with better classification accuracy compared to the state of art solution.