Ship wakes can effectively assist in detecting ship targets at sea due to their large geometric scale, long existence time, non-concealment and strong scattering characteristics. This paper focuses on the Kelvin wake of ship, which is more obvious in the microwave remote sensing image. The geometric model of Kelvin wake is established based on fluid dynamics. Considering the complex dielectric properties of real seawater, the dielectric constants of seawater at different frequencies are calculated by use of the double-Debye model. Considering the two-scale scattering characteristics of random rough sea surface, the spatial distribution of the scattering intensity of the wake is simulated using the semi-deterministic facet scattering model (SDFSM). The effects of ship speed, incident electromagnetic wave frequency and azimuth on the spatial distribution of the scattering intensity of the Kelvin wake at sea are fully studied. This study reveals the formation mechanism of electromagnetic imaging of ship wakes to some extent, and has important application value in the recognition and detection of naval ship targets. It can effectively assist in the establishment of wake geometric model and scattering model database, and realize machine learning with small or zero samples.