A novel technique is developed to reconstruct a nonuniform transmission line by using arbitrary incident waveforms. By discretizing both the incident and reflected waves, we find that the ratio of reflected wave to incident wave has the same form as the reflection coefficient obtained by treating a nonuniform line as a cascaded, multiple-section signal line. A reconstruction scheme is derived to get the impedance profile of a nonuniform line. Some examples are presented to illustrate this new technique.