We developed a reverse-time migration scheme that can image regions with rugged topography without requiring any approximations by adopting an irregular, unstructured-grid modelling scheme. This grid, which can accurately describe surface topography and interfaces between high-velocity-contrast regions, is generated by Delaunay triangulation combined with the centroidal Voronoi tessellation method. The grid sizes vary according to the migration velocities, resulting in significant reduction of the number of discretized nodes compared with the number of nodes in the conventional regular-grid scheme, particularly in the case wherein high near-surface velocities exist. Moreover, the time sampling rate can be reduced substantially. The grid method, together with the irregular perfectly matched layer absorbing boundary condition, enables the proposed scheme to image regions of interest using curved artificial boundaries with fewer discretized nodes. We tested the proposed scheme using the 2D SEG Foothill synthetic dataset.