It is important to analyze the scattering phenomena of a dielectric sphere in conjunction with the improvement of performance of weather radar to observe rain clouds. This paper considers the transient scattering phenomena when a plane electromagnetic pulse wave is incident on a dielectric sphere. Specifically, the responses of the back- and forward-scattering observed at distant points are presented. The response waveforms are compared when the permittivity, loss, and incident waveform are varied. Analyzing the typical response waveforms, the propagation paths were estimated from the characteristics of the response time and waveform so that the scattering phenomena were studied. The fast inversion of Laplace transform (FILT) method was used for the calculation of the transient responses.