We developed a three-dimensional unstructured grid coastal and estuarine circulation model, named the General Ocean Model (GOM). Combining the finite volume and finite difference methods, GOM achieved both the exact conservation and computational efficiency. The propagation term was implemented by a semi-implicit numerical scheme, so-called theta scheme, and the time-explicit Eulerian-Lagrangian Method was used to discretize the non-linear advection term to remove the major limitation of the time step, which appears when solving shallow water equations, by the Courant-Friedrichs-Lewy stability condition. Because the GOM uses orthogonal unstructured computational grids, allowing both triangular and quadrilateral grids, much flexibility to resolve complex coastal boundaries is allowed without any transformation of governing equations. The GOM was successfully verified with five analytical solutions, and it was also validated applying to the Texas coast, showing that overall Skill value of 0.951. The verification results showed that the algorithm used in GOM was correctly coded, and it is efficient and robust.