In this paper, a new approach is presented to model a lightning return-stroke channel and to calculate induced over-voltages on adjacent overhead power transmission lines. In this model, the lightning channel is approximated by a lossy monopole antenna above a perfectly conducting ground. A new electric field integral equation (EFlE) is presented for inductively loaded elements of the channel and its nearby power lines. Solving the new EFIE by the method of moment in time domain, the temporal-spatial current distribution along the lightning chaimel and coupled over voltages on the adjacent metal structures is obtained. An important feature of the proposed model, as opposed to the conventional models, is the fact that the relative permittivity of the surrounding medium equals to unit. In addition, the channel speed can be adjusted using the distributed inductive loads along the channel. The latter enables one to allocate a desired propagation speed to the channel current and the propagated electromagnetic waves. To demonstrate the validity of the model, the current distribution along the channel and the radiated electromagnetic field are computed and compared with the measured data and those obtained using the conventional model. For several power lines, the induced over-voltages are computed and compared with those obtained using the conventional model. It is shown that both the peak value and time duration of the over voltage pulses can remarkably vary. This is sought to be due the effect of propagation speed of the channel current, which can be readily included in the proposed model.