This paper presents an automatic mesh generation procedure on a 2D domainbased on a regular background grid. The idea is to devise a robust mesh generation schemewith equal emphasis on quality and efficiency. Instead of using a traditional regular rectangulargrid, a mesh of equilateral triangles is employed to ensure triangular element of the best qualitywill be preserved in the interior of the domain.As for the boundary, it is to be generated by a node/segment insertion process. Nodes areinserted into the background mesh one by one following the sequence of the domain boundary.The local structure of the mesh is modified based on the Delaunay criterion with the introduc-tion of each node. Those boundary segments, which are not produced in the phase of nodeinsertion, will be recovered through a systematic element swap process. Two theorems will bepresented and proved to set up the theoretical basic of the boundary recovery part. Exampleswill be presented to demonstrate the robustness and the quality of the mesh generated by theproposed technique.