A simple tip leakage flow (TLF) model which consists of a square duct with a longitudinal slit on the top of a side wall is proposed to reproduce the jet flow/main flow shear mechanism of the tip leakage vortex (TLV) rolling-up in turbomachinery. Large-eddy simulation (LES) is employed to investigate the turbulence characteristics of the flow model under low Reynolds number condition. The geometry and boundary conditions of the flow model are simplified from a compressor rotor and modified to apply to low-Re condition for LES. The vortex structures and turbulence characteristics of the LES results are compared with the measurements of the rotor. It is found that the flow model could reproduce similar flow field and turbulence structures compared with the TLF in the real rotor, thus it can be used to investigate the turbulence in practical flows. Reynolds-Averaged Navier-Stokes (RANS) calculations are also carried out. The mean flow and turbulence behaviors of different cases are analyzed. The budgets of turbulent kinetic energy (k) are analyzed to investigate the turbulence transport nature in the TLF model, indicating that the non-equilibrium transport process of k is significant, especially the pressure and turbulent transport, which is not predicted by RANS.