A novel approach for transient analysis of coupled transmission line circuits is presented. While frequency domain response is obtained, it must be transformed to time domain response. The 1-domain modified numerical inversion Laplace transform (NILT) and 2-domain modified NILT are utilized for the time domain response. Then quotient-difference algorithm is used to provide higher speed of calculation and precision of results. Both transient responses on the ends of the transmission lines and along the transmission lines are given. The numerical results prove the new approach is efficient and accurate for treating coupled, lossy, nonuniform and dispersive multiconductor transmission line circuits.