The transient electromagnetic fields of a vertical electric dipole antenna with an impulsive current in a dielectric medium are expressed in an analytical form. It is found that the first part of the electromagnetic fields of the excited electromagnetic pulse is an impulsive wave, which propagates with the speed 1=p(The symbol is abbreviated) and decays exponentially. The other part builds up gradually and propagates slowly, and attenuates with a much lower rate than exponential decay.