We use the semi-classical random laser model, which is described by the Maxwell equations and the rate equations, and utilize the finite-difference time-domain method (FDTD) to investigate the differential characteristic of one-dimensional random laser. The results of the calculation indicate that emitting frequency changes continuously with the slight modification of the thickness of film. Thereby, the random laser is a stable system, not a chaotic system. Those thin films in the center of localized regime have stronger effect on the emitting frequency than those beyond the position of localized regime. The thin films in the center of localized regime form a resonant cavity actually and those thin films beyond the position of localization form reflecting mirrors of cavity. Modifying the thickness of the thin films in the center of the localized regime mean modification of the length of cavity, consequently the emitting frequency is changed. Modification of thickness of the thin films out of localized regime mean change of the reflectivity of the reflecting mirrors of cavity. So it has no effect on the emitting frequency, but it affects the emitting energy of laser. If the modification of the thickness is very great, it maybe changes the position of the localized regime and the emitting frequency of mode.