This study introduces a new version of a virtual tetrahedral gap element to connect partitioned structures which are independently discretized with tetrahedral elements. Tetrahedral meshes are widely used for practical engineering problems due to their simplicity. The proposed interface method employs the localized Lagrange multiplier method. The virtual tetrahedral gap elements are placed between the frame-slave and frame-master interfaces. The surface of the tetrahedral meshes is triangular; thus, a virtual tetrahedral gap element is developed. A distinct feature of the virtual tetrahedral gap element is that it has a zero-strain condition which provides the exact interface reaction forces at the non-matched interface. The proposed tetrahedral gap element handles three-dimensional interface problems more effectively than conventional segment-to-segment methods. It also provides better accuracy. The validity and robustness of the proposed method are demonstrated by several numerical examples.