As a cold and dry planet, Mars contains water resources in the form of water ice, so that the electromagnetic waves can be transmitted to the deep underground to get the information of the topography and subsurface geological structure. Subsurface penetrating radar(SPR) can be widely used in deep space exploration for a long time because of its non-destructive detection mode and its working characteristics not limited by visible light. It is an important type of equipment for detecting the subsurface structure of planets. Orbiter radar is mainly used in Mars exploration. However, because of its low resolution, it is difficult to describe the near surface structure, so there is a lack of radar data which can reflect the shallow information. In this paper, a three-dimensional near surface model of Utopia Planitia on Mars is established. In order to make the simulation results more reasonable, the key factors such as topographic relief, subsurface rocks and water ice, and the variation of dielectric constant in different layers are taken into account. Then the full polarization forward modeling is carried out by using the three-dimensional finite-difference time-domain method. The acquired full polarimetric subsurface penetrating radar(FP-SPR) data with noise is preprocessed and further processed by Pauli decomposition. The underground reflection can be picked up more clearly from the Pauli decomposition results. This work is helpful to identify more details of subsurface structures and provides a reference for the measured data in the future.