Diabetic Macular Edema (DME) is an advanced stage of diabetic retinopathy where the microaneurysms from the retinal vessels may leak fluid or blood into macula the central part of retina. This may cause serious damage to the eyes which may eventually lead to blindness. Therefore, determining the stages of DME is an open research problem. In this work, we proposed a deep learning-based method to identify DME with grading based on non-mydriatic retinal fundus images. We applied multiple image augmentation techniques, such as cropping, resizing, and flipping. Then the preprocessed images were used to train convolutional neural network (CNN)-based model to detect DME and determine the level of grading: Grade 0, Grade 1, and Grade 2. We trained and tested our model using multiple pre-trained CNNs i.e., AlexNet, ResNet18, ResNet34, DenseNet121, DenseNet161, VGG11_bn, VGG16_bn, SqueezeNet, and Inception. Out of all the models VGG16 showed the best accuracy of 96%, sensitivity of 95.8%, and specificity of 96.9%. A comparison against the state-of-the-art methods for DME staging prediction from non-mydriatic images reveal that our approach outperformed the existing methods. The proposed model was developed for non- mydriatic images collected the from IDRID dataset which makes it suitable for its application in clinics lacking proper ophthalmology facilities as well as in remote area lacking a proper ophthalmology clinic.