Abstract: The multi-material problems under high-explosive detonation driving exist extensively in the engineering applications. Lagrangian method has been applied widely in the numerical simulation of these problems, because it can simulate the material interface with high fidelity. Refining mesh is one of the common ways to improve the simulated accuracy. However when the resolution is improved through the global mesh refinement, the robust and the efficiency of Lagrangian calculation become worse. It is very necessary to develop an unstructured multi-level adaptive mesh refinement (AMR) method based on the Lagrangian hydrocode for the multi-material and multi-block problems. In present study, a new AMR strategy is proposed, where an unstructured hierarchical data structure is designed. The multi-level meshes are stored in the unstructured hierarchical data structure, and then they are flattened onto the finest global unstructured mesh for the Lagrangian calculation. To adapt the multi-material and multi-block problems, an adaptive coupling algorithm with sliding interface is developed. This implementation preserves the benefits of an unstructured hierarchical data structure. It also avoids the complexity of time adaption and interlevel coupling using boundary conditions in moved Lagrangian mesh, when the solutions are obtained on every level of a refinement hierarchy. At the same time, this new AMR method can be well adapted to multi-block and multi-material problems. The correctness of the unstructured Lagrangian AMR method is verified by the 1D and 2D detonation problems. A series of multi-material problems under high-explosive detonation driving, including multi-material corner detonation, multi-block multi-material problem and detonation propagation in the small curved channel and so on, are simulated using the proposed unstructured AMR. The numerical results show excellent compatibility and performance for the different complex multi-material problems, and it can save more than 90% of the mesh number. The research is an important foundation for further research on the physics mechanism of detonation constraint problem.