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It is challenging for the mobile robot to achieve autonomous and mapless navigation in the unknown environment with uneven terrain. In this study, we present a layered and systematic pipeline. At the local level, we maintain a tree structure that is dynamically extended with the navigation. This structure unifies the planning with the terrain identification. Besides, it contributes to explicitly identifying the hazardous areas on uneven terrain. In particular, certain nodes of the tree are consistently kept to form a sparse graph at the global level, which records the history of the exploration. A series of subgoals that can be obtained in the tree and the graph are utilized for leading the navigation. To determine a subgoal, we develop an evaluation method whose input elements can be efficiently obtained on the layered structure. We conduct both simulation and real-world experiments to evaluate the developed method and its key modules. The experimental results demonstrate the effectiveness and efficiency of our method. The robot can travel through the unknown uneven region safely and reach the target rapidly without a preconstructed map.