This communication introduces a high-gain antenna designed for satellite communications (SatCom) in the K/Ka band, covering the frequency range 17–31 GHz. The antennas based on a long slot array, fed by a corporate feed network (CFN). The CFN is tapered to reduce sidelobe levels (SLL) in the radiating plane orthogonal to the long slots across the entire frequency band (<-23 dB). Additionally, a pillbox coupler serves as a line source generator to illuminate the CFN, featuring an integrated parabolic reflector illuminated by a displaceable H-plane horn in its focal plane. The antenna is fabricated using computer numerically controlled (CNC) milling technology in Aluminum to minimize losses. The total size of the antenna is 44.5×33.1×6.2 λ30 with λ0 the free space wavelength at 31 GHz. The antenna exhibits a minimum measured realized gain of 34.3 dBi at 17 GHz. The antenna can steer its main beam along the slot plane to cover a field of view exceeding 50° in elevation by displacing the H-plane horn in the focal plane of the pillbox coupler.