Ar gas is known to be rarefied in front of a magnetron sputtering cathode due to the collisional heating by energetic sputtered atoms. The effects of the Ar rarefaction in a magnet-on sputtering apparatus used for Ti-film deposition were investigated using the direct simulation Monte Carlo (DSMC) method which is capable of taking gas rarefaction effects into account. The calculated film deposition rate on a substrate and the film coverage in a small hole were larger than those calculated by the conventional simulation where the gas rarefaction is not included. This shows that the gas rarefaction improves both the film deposition rate and the film coverage.