A Monte-Carlo computer simulation has been performed to describe, at atomic level, the growth of titanium nitride films formed by ion beam enhanced deposition (IBED). The simulation is based on a random target, fixed free path of moving particles and binary collisions. An alternate process of deposition of titanium atoms and implantation of nitrogen ions is applied instead of the actual continuous and synchronous process of IBED. According to the actual conditions, the adsorption of nitrogen gas, which is leaked out from the ion source, at the fresh titanium layer surface has been considered. In addition, the change of the composition profile and the density profile during film growth is taken into account. It is demonstrated that the width of the intermixed region between the film and substrate increases with the increase of the atomic arrival ratio, R, of implanted nitrogen ions to deposited titanium atoms. When the titanium deposition rate is low, the nitrogen concentration of the film is relatively insensitive to R, indicating that a dominant contribution to the nitrogen concentration is derived from the nitrogen gas leaked out from the ion source. The results obtained in this study are in agreement with the experimental measurements.