Abstract: In order to solve the non-physical oscillation problem of the traditional finite difference time domain(FDTD) scheme at the discontinuous solution, the L-stable single step multistage block method is proposed to analyze the time domain transient response of multiconductor transmission lines. In order to avoid the repeated inversion of the coefficient matrix of the system state equation when the boundary conditions are imposed, the more general Sherman-Morrison formula is used to solve the inverse matrix of the coefficient matrix after the boundary conditions are applied. This method is used to simulate uniform lossless multiconductor transmission lines (MTLs) and non-uniform lossy MTLs, and its simulation result is compared with the results given by FDTD algorithm. The results showed that the single step multistage block method can effectively suppress the numerical oscillation and is not limited by step size of simulation in time domain.