The three-fluid model is one of the most advanced models for phenomenologically analyzing annular mist flow. However, a numerical solution based on the three-fluid model often suffers from unclarified numerical instability. The numerical stability was therefore analyzed in the present study using the minimum relaxation distance of the three-fluid model for the annular mist flow in a vertical heated channel. This analysis made it clear that the instability is apt to occur at the onset of the annular flow and in the vicinity of the dryout location. It was also clarified that the virtual mass force has little effect on the improvement of the numerical stability. Then, a partially implicit method for momentum transfer terms was applied to the numerical integration of the three fluid model. It was confirmed that the numerical stability is improved by this method without increasing the difficulty of the programming.