To analyze the effect of the uncertainty of cable structure parameters on terminal voltage under the coupling of multi-conductor transmission lines, a method of Chebyshev polynomial approximation based on interval analysis is introduced. Firstly, the telegraph equation of transmission line is transformed into an ordinary differential equation. Secondly, the extension function of the telegraph equation is obtained by Chebyshev polynomial, and then the fluctuation range of terminal voltage is obtained. Compared with the mixed polynomial method and MC (Monte Carlo) method, this method only needs to input the range of fluctuation of random parameters. The multi-conductor wire beam with random variation of height and spacing under electromagnetic pulse irradiation was simulated. The simulation results show that the distance has little effect on terminal voltage, and the terminal voltage is more sensitive to height. Under the condition that the calculated results are in agreement with each other, the computation time of Chebyshev polynomial approximation method is much less than that of MC method.