Abstract: A time-dependent electromagnetic field code is developed in this paper and is applied to simulate time-space characteristics of elves （emission of light and very low frequency perturbations from electro-magnetic pulse sources）. The simulation results indicate the electric fields produced by thunderstorm discharge include the Quasi-Electrostatic Fields （QEF） and the radiation fields. The radiation fields, which are produced by the discharge current pulse, directly produce the elves. The distributions of radiation fields are similar to the electric fields produced by the electric dipole radiation. The radiation fields above the thunderstorm discharge are relatively weaker, but the radiation fields are relatively greater near the ground. Moreover, the simulation results show that the double or single ring structure of optical emission, which corresponds to the double or single peak structure of elves, will appear on the film of a camera. During the outward expanding process of elves at the altitude of 83km, the intensity of optical emission originally increases with the radial distance till it gets the maximum, then decreases with the radial distance. In addition to, the causes that the expanding velocity of elves is bigger than the speed of light are explored using the assumption of spherical electromagnetic wave.