The topography has serious effects on time-domain airborne electromagnetic (AEM) signal, and the EM responses resulted from the topography frequently overwhelm those from the underground abnormal bodies. This brings big challenges to the traditional AEM interpretations based on a flat ground model. In this article, we develop a 3-D AEM inversion algorithm for a topographic earth model. The time-domain finite-element algorithm based on unstructured mesh is used to model the AEM responses. The tetrahedral grids provide the flexibility to fit the rugged topography. Furthermore, we adopt the Gauss–Newton method for our inversion of time-domain AEM data. In the forward modeling and the calculation of Jacobian matrix, we introduce an unstructured local mesh and decouple the meshes for forward modeling and inversion to improve the computational efficiency. For that purpose, we first set up an unstructured inversion mesh and then extract those cells corresponding to the sensitive area of AEM system for each survey station from the inversion mesh and construct a local forward mesh with the extracted cells as the core. After that, we take advantage of the spatial relationship between the local forward meshes and the inversion ones to set up the global sensitivity matrix for Gauss–Newton inversion. We test the effectiveness of our algorithm by applying our 3-D inversion code to both synthetic and survey data. The numerical experiments show that the Earth topography can have big influence on AEM inversions, and ignoring the topography can create serious distortion to AEM inversion results.