Background and objective: The Covid-19 pandemic significantly affects the global population’s fitness and day-to-day life. The necessary action to fight against Covid is to have a fast, accurate and affordable diagnosis system. Most of the diagnostic systems available today have a low detection rate and are time consuming. Hence, there is a demand to design an affordable, accurate, and fast diagnostic system for Covid. The diagnostic system that uses the Convolutional Neural Network (CNN) does not consider the complex correlation of multimodal image data, thus misleading the diagnostic results. Graph Convolutional Network (GCN) provides a better solution for the complex representation of data, as it is modeled based on the pairwise relationship in the image features. Method: Diagnosis of Covid, Parasite, or Lung Tumor from X-ray images needs a more complex representative model. There is a demand to categorize the images grounded on highly complex features. To solve the issue mentioned earlier, this work proposes a Hypergraph- and convolutional neural network-based Fast and Accurate Diagnosis (FAT) system for Covid. The in-depth features are mined using a residual neural network from the X-ray images. The learning-based method optimizes a high-level correlation in the deep structures by constructing it as a hypergraph. Results: The proposed method is assessed based on the Covid dataset. The experimental outcomes show that the proposed system FAT provides the accuracy of 99.8%, sensitivity of 99.5%, and specificity of 99%. It outperforms all the current diagnosis systems for Covid. Conclusion: The proposed deep learning-based model is well suited for Covid diagnosis at the preliminary level. It allows diagnosing Covid by low radiation chest X-ray images with higher accuracy.