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The spatial dispersion significantly limits the operating bandwidth of a large-aperture reflectarray antenna. To achieve a wideband high-gain reflectarray antenna, a design method is proposed based on the spatial dispersion compensation concept. By introducing different resonant structures in reflectarray elements, each element has the ability to track the desired frequency–phase response, which means that the spatial dispersion of the large-aperture reflectarray antenna can be compensated by the phase dispersion of the reflectarray element over the entire frequency band. Thus, a wideband high-gain reflectarray antenna can be realized by the use of single-layer elements. As an example, a center-fed reflectarray antenna with a diameter of 354 mm ($35.4\lambda _{0}$ at 30 GHz) and a focal length to diameter ratio of 0.97 is designed and fabricated. The measured maximum gain of the prototype reflectarray antenna is 37.8 dBi with a 1 dB bandwidth of 26.7%, i.e., from 26.5 to 34.5 GHz. Compared with other high-gain single-layer reflectarray antennas, this type of antenna presents better performance. [ABSTRACT FROM AUTHOR]