A novel strategy,which includes the statements of the no-cavity and nonoverlapping conditions and a mesh generation approach, is presented to create unstructured triangular and tetrahedral meshes. For this strategy, the no-cavity and nonoverlapping conditions provide the theoretical basis for the mesh-generation procedure. In this procedure, a structured background grid is utilized to determine the distribution of characteristic lengths, According to this distribution, nodes are generated first. Then, a characteristic-range method and a hybrid method are proposed for connecting these nodes. By the use,of a mesh-removal process, the final mesh is obtained, To illustrate the procedure, a two-dimensional domain with four-element airfoils is considered. For three-dimensional I domains, a postprocessing is introduced to improve the mesh quality. To evaluate the strategy, two concentric cubes, a coaxial annual pipe, and two concentric spheres are considered. For the Bow region around the ONERA M6 wing, the hybrid method with postprocessing is utilized, and the mesh quality is compared to those previously attained. To demonstrate this strategy further, a mesh is generated for the Bow region around an airplane.