A system which uses the non equilibrium fluctuating energy to do work is considered as a result of Brownian motor derived by both internal and external noises. The corresponding diffusion model including damping force and double noise sources is proposed. Through the analytical calculation and numerical simulation, the mechanism of the directed motion of the Brownian motor driven by multiplicative noise and the effect of damping force on the steady current in the one dimensional inertia ratchet potential are accordingly expounded and analyzed. As a application, the experimental phenomenon of the stepping motion of the single motor protein is explained.