<p>The reflection of plane electromagnetic wave on the interface between time-varying medium and time-invariant medium and the propagation of plane electromagnetic wave in time-varying medium are studied in this article. The medium which changes with time as an exponential function is observed and the analytical solution of the electromagnetic wave in such medium is obtained by the method of separation variables. The transient reflection coefficient on the surface of the time-varying medium and the transient transmission coefficient in time-varying medium are obtained for the first time by taking the limit for time increment. The validity of the solution is testified by three approaches. The propagation characteristics are discussed by the example in different areas.</p>