This paper presents a universal materials model of deep-learning density functional theory (DFT) Hamiltonian (DeepH), which enables computational modeling of the complex structure-property relationships of materials. The model is trained on a large materials database of approximately 10,000 solid materials, spanning the first four rows of the periodic table. The DeepH-2 method, an advanced equivariant transformer architecture, is used to train the model, incorporating principles of locality and equivariance to improve accuracy and transferability. The model is further refined to address the gauge problem, ensuring that the DFT Hamiltonian is represented accurately despite variations in energy reference. The resulting universal materials model achieves a mean absolute error (MAE) of 2.2 meV, comparable to specific materials models. The model is also fine-tuned for specific materials datasets, such as carbon allotropes, demonstrating its effectiveness in predicting material properties with high accuracy. The work highlights the potential of DeepH in advancing artificial intelligence-driven materials discovery by enabling the development of large materials models that can handle diverse elemental compositions and material structures. The results show that larger training datasets improve model accuracy, and the model's performance is validated through comparisons with DFT calculations for various materials. The study also addresses challenges in training universal materials models, including the need for large datasets and the importance of gauge equivalence in DFT Hamiltonians. The findings demonstrate the feasibility of training a universal materials model of DeepH, paving the way for future research in materials science and AI-driven discovery.This paper presents a universal materials model of deep-learning density functional theory (DFT) Hamiltonian (DeepH), which enables computational modeling of the complex structure-property relationships of materials. The model is trained on a large materials database of approximately 10,000 solid materials, spanning the first four rows of the periodic table. The DeepH-2 method, an advanced equivariant transformer architecture, is used to train the model, incorporating principles of locality and equivariance to improve accuracy and transferability. The model is further refined to address the gauge problem, ensuring that the DFT Hamiltonian is represented accurately despite variations in energy reference. The resulting universal materials model achieves a mean absolute error (MAE) of 2.2 meV, comparable to specific materials models. The model is also fine-tuned for specific materials datasets, such as carbon allotropes, demonstrating its effectiveness in predicting material properties with high accuracy. The work highlights the potential of DeepH in advancing artificial intelligence-driven materials discovery by enabling the development of large materials models that can handle diverse elemental compositions and material structures. The results show that larger training datasets improve model accuracy, and the model's performance is validated through comparisons with DFT calculations for various materials. The study also addresses challenges in training universal materials models, including the need for large datasets and the importance of gauge equivalence in DFT Hamiltonians. The findings demonstrate the feasibility of training a universal materials model of DeepH, paving the way for future research in materials science and AI-driven discovery.