Differential equation based numerical methods such as finite difference time domain (FDTD) need to truncate the solution region in problems with infinite dimensions. In these problems, uniform plane wave illumination causes significant error due to the reflections from truncated boundaries. To tackle this, here, a new incident Gaussian pulse is introduced for the FDTD solution of a three-dimensional multilayered rough surface including a buried object, in the microwave regime. The introduced incident wave is a collimated wave that does not attenuate along its propagation direction and has a Gaussian beamwidth at the surface normal to the propagation direction. This leads to nearly zero reflections from truncated areas and hence, the scattered wave from the buried object can be distinguished more accurately. We show that the difference between the radar cross section (RCS) of a layered ground with and without the buried object is large in comparison to other illuminations. As well, a two-dimension image of the buried object is sketched based on the magnitude of the scattered field. In this regard, different cases such as some simple buried objects, water leakage from a buried pipe and a hollow in the ground are studied.