Radar polarimetry, i.e., the full utilization of vector nature of electromagnetic wave information, has become an indispensable tool for advanced radar systems. If the principle of radar polarimetry could be incorporated into a wideband FM-CW radar, it would become a highly advanced imaging system in the short range region, since the FM-CW radar utilizes the continuous wave principle for which the range resolution is determined by the frequency resolution. It also has the potential for precisely measuring distances in the near range with considerably simple equipment compared to pulsed radar systems. This paper applies the principle of radar polarimetry to a synthetic aperture FM-CW radar and presents a two-dimensional (2-D) full polarimetric imaging result of linear targets. It is shown that the polarimetric target reflection coefficients obtained by the synthetic aperture FM-CW radar act as elements of the Sinclair scattering matrix, although the coefficient is derived by a wideband signal. Using the scattering matrix optimization procedure, a 2-D polarimetric imaging experiment of an orthogonally placed linear target set was successfully carried out in a laboratory at a frequency of 8.2-9.2 GHz.