This paper proposes an unstructured tetrahedral meshing algorithm for CAD models in the IGES format. The work presented is based on the advancing front method, which was proposed by the third author. Originally, the advancing front method uses three basic operators, namely, trimming, wedging, and digging. In this research, in addition to the basic operators, three new operators splitting, local finishing, and octahedral-are added to stabilize the meshing process. In addition, improved check processes are applied to obtain better-shaped elements. The algorithm is demonstrated and evaluated by four examples.