A numerical method based on a finite volume approach has been developed to predict the rotordynamic forces on an eccentric labyrinth seal. The SIMPLER algorithm and a low-Reynolds-number κ-ε turbulence model are used to compute the complex turbulent flow field within the seal. To verify the validity of the developed method, the turbulent flow in the labyrinth seal was calculated and the resulting fluid forces was estimated. The predicted fluid forces are in good agreement with the reported measured values. It is also shown that the flow field near each labyrinth tooth must be accurately predicted to evaluate the rotordynamic forces. Labyrinth tooth throttling has more effect on the tangential force component than on the radial one. The developed code was proven to be an effective tool for predicting rotordynamic forces.