This paper presents a flat, high gain, wide scanning, broadband continuous transverse stub (CTS) array. The design procedure, the fabrication, and an exhaustive antenna characterization are described in details. The array comprises 16 radiating slots and is fed by a corporate-feed network in hollow parallel plate waveguide (PPW) technology. A pillbox-based linear source illuminates the corporate network and allows for beam steering. The antenna is designed by using an ad hoc mode matching code recently developed for CTS arrays, providing design guidelines. The assembly technique ensures the electrical contact among the various stages of the network without using any electromagnetic choke and any bonding process. The main beam of the antenna is mechanically steered over ±40° in elevation, by moving a compact horn within the focal plane of the pillbox feeding system. Excellent performances are achieved. The features of the beam are stable within the design 27.5-31 GHz band and beyond, in the entire Ka-band (26.5-40 GHz). An antenna gain of about 29 dBi is measured at broadside at 29.25 GHz and scan losses lower than 2 dB are reported at ±40°. The antenna efficiency exceeds 80% in the whole scan range. The very good agreement between measurements and simulations validates the design procedure. The proposed design is suitable for Satcom Ka-band terminals in moving platforms, e.g., trains and planes, and also for mobile ground stations, as a multibeam sectorial antenna.