For a single-polarization-truncated-cone-phased array antenna stimulated by horizontal or vertical polarized dipoles, the spatial polarization characteristics are modeled when the array antenna electronically scans in space. The theoretical analysis and simulations show that: the spatial polarization ratio of a single-polarization-truncated-cone-phased array monotonically increases as the angles between the pointing angles or observation angles and the normal increases; the spatial polarization ratio monotonically decreases as the slope angles decrease; the patterns of a single-polarization-truncated-cone-phased array are related to the polarization of array elements, the pointing angles, and the observation angles; the larger the size of a single-polarization-truncated-cone-phased array antenna is, the more abundant the spatial polarization information is. These conclusions offer a theoretical foundation for studies such as the polarization scattering matrix measurement, the polarization filtering, and the polarimetric anti-jamming based on the spatial polarization characteristics of the single- polarization-truncated-cone-phased array. The conclusions offer a theoretical basis for the studies such as the antenna design, the polarization characteristics analysis and the polarization calibration of the full-polarization-truncated-cone array as well.