In order to explore the leakage characteristics of the labyrinth seal in an offcenter position, ICEM Computational Fluid Dynamics (CFD) software was used. Three dimensional (3D) model of labyrinth seal was divided into structured mesh, and the standard k-ε turbulence model was selected to numercially simulate the labyrinth of different eccentricity with incompressible fluid as the working medium. The influence of different gap and pressure ratio on the leakage characteristics of eccentric labyrinth seal was analyzed. The results show that the leakage of the seal increases with the increase of the gap width when the eccentricity is invariable. Similarly, the leakage of the seal increases with the increase of the pressure ratio increase,and in the high pressure ratio of operating conditions, the leakage with the eccentricity of the change is more obvious.