In this paper, we investigated the influence of time-dependent losing coefficient on the characteristics of the laser mode by solving the rate equations system which describe the variation in photon density of two-mode random laser. The results showed that when the losing coefficient depends on the time of the characteristics of the modes such as the photon density, the time to reach the maximum value of the photon density and the pulse duration of the emitting mode were changed. The received results give us more knowledge about the influence of time-dependent losses on the operation of the two-mode random laser.