Prediction and discovery of new materials with desired properties are at the forefront of quantum science and technology research. A major bottleneck in this field is the computational resources and time complexity related to finding new materials from ab initio calculations. In this work, an effective and robust deep learning-based model is proposed by incorporating persistent homology and graph neural network which offers an accuracy of 91.4% and an F1 score of 88.5% in classifying topological vs. non-topological materials, outperforming the other state-of-the-art classifier models. The incorporation of the graph neural network encodes the underlying relation between the atoms into the model based on their own crystalline structures and thus proved to be an effective method to represent and process non-euclidean data like molecules with a relatively shallow network. The persistent homology pipeline in the suggested neural network is capable of integrating the atom-specific topological information into the deep learning model, increasing robustness, and gain in performance. It is believed that the presented work will be an efficacious tool for predicting the topological class and therefore enable the high-throughput search for novel materials in this field.