One of commonly physical phenomena encountered in pump sump systems in which its significant influence to the hydraulic performance of pump system plays an important role in the field of fluid engineering, is the appearance of free surface and submerged vortices. In this paper, a study of the vortices behavior and their formative mechanism of asymmetry is considered in this paper by using numerical approach. The Reynolds-Averaged Navier-Stokes (RANS) equations and k-omega Shear Stress Transport turbulence model used to describe the properties of turbulent flows, in company with VOF multiphase model, are implemented by Fluent code with multi-block structured grid system. In the numerical simulation, the calculated elevation of air-water interface and vortex core contours are used to classify visually surface vortices as well as submerged vortices. It is shown that the free surface vortex is identified by the concavity of liquid region from the free surface and swirling flow at that own plane. To investigate the distinctive behavior of these vortices corresponding to each given flow rate at the same water level, some numerical testing of them are considered here in such a manner that the flow pattern of surface vortex are obtained similarly to the obtained results from experiment. Furthermore, the influence due to the change of grid refinement and the variation of depth of the concavity are also considered in this paper. From that, these influential factors will be implemented to design a good pump sump with higher performance in the future.