Abstract: In view of the fluctuating propagation of voltage/current wave in transmission line, a generalized time-fractional equation is used for transmission line to express the abnormal diffusion process of the voltage/current wave. Introducing the Adomian decomposition method, transient analysis is made to the generalized equation with a simulation done as instance for lossless transmission line. Simulation results showed that introducing the derivative of the time-fractional equation into the lossless transmission line model is available to express well the transient characteristics of the propagation/diffusion process of voltage/current wave in such a line, and it is of practical importance to the transient analysis of transmission line. In comparison with the conventional fractional Laplace algorithm, the method proposed is shorter in simulating time, and simpler in computation with less data required.