In this paper, one of the most modern random lasers known as random distributed feedback fiber laser is investigated when the third-order dispersion (TOD) is taken into account. The laser characteristics are simulated based on the nonlinear Schrödinger equations (NLSEs) where the power evolution of three interacting waves: the pump, the forward and the backward Stokes waves, are investigated as they propagate down the fiber. The results show that due to TOD, the output characteristics of the laser are changed and particularly, the output power becomes asymmetrical. Moreover, the impacts of fiber nonlinear coefficient and input power on the output power and the output spectrum are studied.