Eczema is the most common among all types of skin diseases. A solution for this disease is very crucial for patients to have better treatment. Eczema is usually detected manually by doctors or dermatologists. It is tough to distinguish between different types of Eczema because of the similarities in symptoms. In recent years, several attempts have been taken to automate the detection of skin diseases with much accuracy. Many methods such as Image Processing Techniques, Machine Learning algorithms are getting used to execute segmentation and classification of skin diseases. It is found that among all those skin disease detection systems, particularly detection work on eczema disease is rare. There is also insufficiency in eczema disease dataset. In this paper, we propose a novel deep CNN-based approach for classifying five different classes of Eczema with our collected dataset. Data augmentation is used to transform images for better performance. Regularization techniques such as batch normalization and dropout helped to reduce overfitting. Our proposed model achieved an accuracy of 96.2%, which exceeded the performance of the state of the arts.