Accurately and efficiently tracking the interface motion is of great importance in multiphase flow simulations. We propose a novel Front-Tracking method, the Edge-Based Interface Tracking (EBIT) method, to address this challenge. In the EBIT method, marker points are exclusively placed on the grid edges, and their connectivity is implicitly described using a local data structure, so-called Color Vertex. The interface is advected using a split scheme. To maintain the correspondence between markers and cell edges, we carry out a reconstruction step at the end of each advection step. This step computes the updated positions of markers on the cell edges, transforming the Lagrangian markers into an Eulerian field. This transformation facilitates the parallelization of the EBIT method, particularly when coupled with quad-/octree meshes, offering efficiency over traditional Front-Tracking methods. In this work, we further propose a simplified strategy to extend the EBIT method to three dimensions (3D). The directional split scheme used in the 2D version is directly generalized to 3D. Specifically, the 3D advection within a cubic cell along a given direction is decomposed into two 2D advection problems on the corresponding cube faces. This dimension reduction allows us to fully reuse the 2D interface reconstruction algorithms, substantially simplifying the implementation. To validate the proposed solver, we conduct a series of kinematic and dynamic test cases and compare the results with those obtained using the PLIC-VOF method. Furthermore, we demonstrate the scalability of the EBIT method on up to 4,096 CPU cores.