The paper proposes an electromagnetic-wave beam-scanning antenna system using a simple rotation of a pair of near-field graded-dielectric plates (GDPs). The antenna system requires an electromagnetic (EM) illuminator, with nearly symmetric aperture field distribution, as the base antenna and two types of GDPs: one radially graded dielectric (RGD) and two linearly graded dielectric (LGD) plates. The RGD first focuses the beam of the base antenna in the broadside direction, and the LGD then tilts the focused beam at an offset angle. For some types of base antennas, having fairly uniform aperture phase distributions, an RGD may not be required and only a pair of LGDs are sufficient. Irrespective of the antenna configuration, using a simple rotation of the two LGDs, the beam can be scanned to any position within a large conical region. The antenna system presented as a proof of concept has a resonant-cavity antenna as the base antenna and three graded-dielectric plates. The aperture length of the antenna system is 6λ0 and its height is 2.2λ0. The results predicted by numerical simulations indicate that the antenna system has highest peak directivity of 21 dBi. The beam can be scanned to any direction within a cone having an apex angle of 20º.