A singly fed wideband circularly polarized (CP) substrate-integrated dielectric resonator antenna (SIDRA) is proposed for millimeter-wave (mm-wave) applications. The SIDRA consists of an inner cylindrical dielectric resonator (DR), an outer ring DR, and a substrate-integrated waveguide (SIW) cavity. To generate CP fields, a cross-slot formed by two rectangular slots with different lengths is utilized to feed the DRA at its bottom. It has been found that owing to the embedded structure, the fundamental HEM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{11\delta }$ </tex-math></inline-formula> mode of the inner DR and the higher order HEM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{12\delta +1}$ </tex-math></inline-formula> mode of the entire DR can be excited simultaneously, at adjacent frequencies. Moreover, owing to the different loading effects of the two feeding slots, the resonance frequencies of the nearly degenerate DR modes excited by the two slots are slightly different from each other. The two nearly degenerate modes lead to the wide impedance and axial ratio (AR) bandwidths of 34.6% and ~30%, respectively. In addition, due to the surrounding SIW cavity, the directivity of the antenna is greatly improved as compared with that of the isolated counterpart, with the maximum gain given by 8.15 dBic.